Free Printable 12 : QUIZ : STRAIGHT LINES: 10 JAN

1.

Cartesian - form- of - line
through (5, 2, - 4)
and - parallel - to
vector

3i+2j-8k,\ \ is

a)

$\frac{x-5}{3}=\frac{y-2}{2}=\ \frac{z+4}{\ 8}$

b)

$\frac{x-5}{3}=\frac{y-2}{2}=\ \frac{z+4}{-\ 8}$

c)

$\frac{x-5}{3}=\frac{y+2}{2}=\ \frac{z+4}{-\ 8}$

d)

$\frac{x+5}{3}=\frac{y-2}{2}=\ \frac{z+4}{-\ 8}$

2.

vector - form - of

\frac{x+3}{2}=\frac{y-5}{4}=\frac{z+6}{2}

is

a)

$\overrightarrow{r\ }\ =\ 3i+5j-6k+\lambda\left(2i+4j+2k\right)$

b)

$\overrightarrow{r\ }\ =\ -3i-5j-6k+\lambda\left(2i+4j+2k\right)$

c)

$\overrightarrow{r\ }\ =\ -3i+5j-6k+\lambda\left(2i+4j+2k\right)$

d)

$\overrightarrow{r\ }\ =\ -3i+5j-6k+\lambda\left(2i+4j-2k\right)$

3.

Distance - between - lines

\overrightarrow{r\ }\ =\ \overrightarrow{a_1}\ +\ \lambda\overrightarrow{b\ _{ }}

&

\overrightarrow{r\ }\ =\ \overrightarrow{a_2}\ +\ \mu\ \overrightarrow{b_{ }}

is

a)

0

b)

$\left|\frac{\overrightarrow{b\ }\times\left(\overrightarrow{a_2}-\ \overrightarrow{a_1}\right)}{\left|\overrightarrow{a_1\ }\right|}\right|$

c)

$\left|\frac{\overrightarrow{b\ }\times\left(\overrightarrow{a_2}-\ \overrightarrow{a_1}\right)}{\left|\overrightarrow{a_2}\right|}\right|$

d)

$\left|\frac{\overrightarrow{b\ }\times\left(\overrightarrow{a_2}-\ \overrightarrow{a_1}\right)}{\left|\overrightarrow{b\ }\right|}\right|$

4.

$Equation\ -\ of\ -\ plane$
$pas\sin g\ \ -\ though,\ \ \overrightarrow{a\ }\ \ \&$
$perpendicular\ ,\ \ to\ \ \overrightarrow{N\ }\ is$

a)

$\overrightarrow{r\ }.n\ \ =\ a$

b)

$\left(\overrightarrow{r\ }\ +\ \overrightarrow{a\ }\right).\overrightarrow{N\ }\ =\ 0$

c)

$\left(\overrightarrow{r\ }\ -\ \overrightarrow{a\ }\right).\overrightarrow{N\ }\ =\ 0$

d)

$\left(\overrightarrow{r\ }\ -\ \overrightarrow{N\ }\right).\overrightarrow{a\ }\ =\ 0$

5.

$Line\ -\ pas\sin g\ -\ through$
$\overrightarrow{a\ }\ \ \&\ \ \overrightarrow{b\ }\ is$

a)

$\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\ \overrightarrow{b\ }$

b)

$\overrightarrow{r\ }\ =\ \overrightarrow{b\ }+\ \lambda\ \overrightarrow{a\ }$

c)

$\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\left(\ \overrightarrow{b\ }+\ \ \overrightarrow{a\ }\right)$

d)

$\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\left(\ \overrightarrow{b\ }-\ \ \overrightarrow{a\ }\right)$

6.

Direction - ratio - of

line

6x - 2 = 3y + 1 = 2z - 2

is

a)

1, 2 , 3

b)

3, 2, 1

c)

5, 6 ,7

d)

7, 8 , 9

7.

Direction - cosines - of
line

\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}

is

a)

$-\ \frac{3}{7},\ \frac{6}{7},\ -\frac{3}{7}$

b)

$-\ \frac{2}{7},\ \frac{6}{7},\ -\frac{3}{9}$

c)

$-\ \frac{2}{7},\ \frac{5}{7},\ -\frac{3}{7}$

d)

$-\ \frac{2}{7},\ \frac{6}{7},\ -\frac{3}{7}$

8.

Direction - ratio - of
line

x\ =\ ay\ +\ b,\ \ z\ =\ cy+d\

is

a)

a, 1, c

b)

1, 1, 1

c)

a, c, 1

d)

c, 1, a

9.

Line - through (1, 2, 3)
and - parallel - to

\frac{-x-2}{1}=\frac{y+3}{7}=\frac{2z-6}{3}

is

a)

$\frac{x-1}{1}=\frac{y-2}{7}=\frac{z-3}{3}$

b)

$\frac{x-1}{1}=\frac{y-2}{14}=\frac{z-3}{3}$

c)

$\frac{x-1}{1}=\frac{y-2}{7}=\frac{z-3}{-\ 3}$

d)

$\frac{x-1}{-2}=\frac{y-2}{14}=\frac{z-3}{3}$

10.

\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\ \overrightarrow{b\ }

is

a)

$line\ through\ \overrightarrow{\ a\ \ }\$
$and\ \overrightarrow{b\ }$

b)

$line\ through\ \overrightarrow{\ b\ \ }\$
$and\ \parallel\ to\ \overrightarrow{a\ }$

c)

$line\ through\ \overrightarrow{\ a\ \ }\$
$and\ \parallel\ to\ \overrightarrow{b\ }$

d)

$line\ \parallel\ to\ \ \overrightarrow{\ a\ \ }\$
$and\ \overrightarrow{b\ }$

11.

$A\ point\ on$
$\frac{x\ -\ x_1}{a}=\frac{y\ -\ y_1}{b}\ =\ \frac{z\ -\ z_1}{c}$
is

a)

$\left(x_1+a,\ y_1+\ b,\ z_1+\ c\right)$

b)

$\left(x_1+\lambda a,\ y_1+\ \lambda b,\ z_1+\ \lambda c\right)$

c)

$\left(\lambda x_1+a,\ \lambda y_1+\ b,\ \lambda z_1+\ c\right)$

d)

$\left(\lambda x_1+\mu a,\ \lambda y_1+\ \mu b,\ \lambda z_1+\ \mu c\right)$

12.

Equation of line

through,\ 2i-j+4k

and - in the - direction - of

$i+j-2k$

is

a)

$\frac{x-2}{1}=\frac{y+1}{1}=\ \frac{z-4}{-2}$

b)

$\frac{x-2}{1}=\frac{y+1}{1}=\ \frac{z-4}{2}$

c)

$\frac{x-2}{1}=\frac{y-1}{1}=\ \frac{z-4}{-2}$

d)

$\frac{x+2}{1}=\frac{y+1}{1}=\ \frac{z-4}{-2}$

13.

$Direction\ -\ ratio\ -\ of$
$line,\ 6x\ =\ 3y\ =\ 2z$
is

a)

1 , 2 , 3

b)

3, 2 , 1

c)

1, 1 , 1

d)

0, 1 , 0

14.

Direction - ratio - of

x = ay , z= cy , is

a)

1, 2, a

b)

1, a, c

c)

c, 1, a

d)

a, 1, c

15.

Line - through
(1, 2, - 4)

and,\ \parallel\ to,\ \frac{x-3}{4}=\ \frac{y-5}{2}=\ \frac{z+1}{3}

a)

$\frac{x-1}{4}=\ \frac{y-2}{2}=\ \frac{z+4}{3}$

b)

$\frac{x-1}{4}=\ \frac{y-2}{-2}=\ \frac{z+4}{3}$

c)

$\frac{x-1}{4}=\ \frac{y-2}{2}=\ \frac{z+4}{-\ 3}$

d)

$\frac{x_{ }+1}{4}=\ \frac{y-2}{2}=\ \frac{z+4}{3}$

16.

lines

\frac{x}{1}=\ \frac{y-2}{2}=\frac{z+3}{3}

and,

\frac{x-2}{2}=\ \frac{y-6}{3}=\frac{z-3}{4}

intersects - at

a)

( 1, 2 , 3 )

b)

( 2 , 6 , 3)

c)

( 5, 6, 9)

d)

( 11, 13, 8)

17.

$\frac{x-3}{3}=\frac{\ y-\ 2}{1}=\ \frac{z-1}{0}$
is

a)

$\parallel\ -\ to\ -\ x\ -\ axis$

b)

$\parallel\ -\ to\ -\ y-\ axis$

c)

$\parallel\ -\ to\ -\ z\ -\ axis$

d)

$\perp\ ,\ \ to\ -\ z\ -\ axis$

18.

Lines

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}

and,\ \frac{x-1}{-2}=\frac{y-2}{-\ 4}=\frac{z-1}{-\ 6}

are

a)

parallel

b)

perpendicular

c)

skew

d)

intersecting

19.

Equation - of - x - axis

is

a)

$\frac{x-0}{1}=\ \frac{y-0}{0}=\frac{z-0}{0}$

b)

$\frac{x-0}{0}=\ \frac{y-0}{1}=\frac{z-0}{0}$

c)

$\frac{x-0}{0}=\ \frac{y-0}{0}=\frac{z-0}{1}$

d)

$\frac{x-0}{0}=\ \frac{y-0}{0}=\frac{z-0}{0}$

20.

Distance - of $,\left(\alpha,\ \beta,\ \gamma\right)$
from
y - axis - is

a)

$\beta$

b)

$\left|\beta\right|$

c)

$\left|\alpha\right|+\left|\beta\right|$

d)

$\sqrt{\alpha^2+\gamma^2}$

21.

Distance - of - plane
$\overrightarrow{r\ }.\left(\frac{2}{7}i+\frac{3}{7}i-\frac{6}{7}k\right)=\ 1$
from - origin - is

a)

1

b)

7

c)

$\frac{1}{7}$

d)

5

22.

$Direction\ -\ ratio\ -\ of$
$line\ ,\ \frac{4-x}{2}=\ \frac{y}{6}=\ \frac{1-z}{3}$
is

a)

- 2, 6 , - 3

b)

2 , 6 , 3

c)

- 2, 6 , 3

d)

2, 6 , -3

23.

Line - parallel - to

2i\ +\ j\ +\ 3k

is

a)

$\frac{x-5}{2}=\ \frac{y-3}{-\ 1}=\ \frac{z}{3}$

b)

$\frac{x-5}{-\ 2}=\ \frac{y-3}{1}=\ \frac{z}{3}$

c)

$\frac{x-5}{2}=\ \frac{y-3}{1}=\ \frac{z}{-\ 3}$

d)

$\frac{x-5}{2}=\ \frac{y-3}{1}=\ \frac{z}{3}$

24.

$Lines\ ,\ \frac{x-1}{-2}=\ \frac{y-4}{3p}=\frac{z-3}{4}\$

and

\frac{x-2}{4p}=\ \frac{y-5}{2}=\frac{z-1}{-7}

are - perpendicular

then, p =

a)

10

b)

- 10

c)

14

d)

- 14

25.

Line, through

\left(\alpha,\ \beta,\ \gamma\right)

and - parallel - to
z - axis, is

a)

$\frac{x-\ \alpha}{0}=\ \frac{y-\ \beta}{0}=\ \frac{z\ -\ \gamma}{1}$

b)

$\frac{x-\ \alpha}{0}=\ \frac{y-\ \beta}{1}=\ \frac{z\ -\ \gamma}{0}$

c)

$\frac{x-\ \alpha}{1}=\ \frac{y-\ \beta}{0}=\ \frac{z\ -\ \gamma}{0}$

d)

$\frac{x-\ \alpha}{1}=\ \frac{y-\ \beta}{1}=\ \frac{z\ -\ \gamma}{1}$

26.

Foot - of - perpendicular

drawn\ -\ from\ \left(2,\ 4,\ -\ 1\right)

to - the - line

\frac{x+5}{1}=\ \frac{y+3}{4}=\ \frac{z-6}{-9}

is

a)

( 4, 1, 3)

b)

( 4, -1 , 3)

c)

( - 4 , 1, - 3)

d)

( - 4, - 1, -3 )

27.

line - through

( 0, - 1, - 1 ) &

( 4, 5, 1 )

is

a)

$\frac{x}{4}\ =\ \frac{y+\ 1}{6}\ =\ \frac{z+\ 1}{2}$

b)

$\frac{x}{4}\ =\ \frac{y-\ 1}{6}\ =\ \frac{z+\ 1}{2}$

c)

$\frac{x}{4}\ =\ \frac{y+\ 1}{6}\ =\ \frac{z-\ 1}{2}$

d)

$\frac{x}{4}\ =\ \frac{y+\ 1}{-\ 6}\ =\ \frac{z+\ 1}{2}$

28.

Direction - ratio - of - line

5x - 3 = 15y + 7 = 3 - 10 z

is

a)

6 , 2 , 3

b)

6 , 2, -3

c)

6, - 2 , 3

d)

6 , - 2 , -3

29.

$line,\ \overrightarrow{r\ }\ -\ \overrightarrow{a\ }\ =\ \lambda.\ \overrightarrow{b\ }$
is - parallel - to

a)

$\ \overrightarrow{a\ }$

b)

$\ \overrightarrow{b\ }$

c)

$\lambda$

d)

None of all

30.

A - line - has

direction - ratios, – 18, 12, – 4

then - its - direction

cosines - are

a)

$\frac{7}{11},\ \frac{6}{11},\ -\ \frac{2}{11}$

b)

$\frac{9}{11},\ \frac{6}{11},\ -\ \frac{2}{11}$

c)

$-\ \frac{9}{11},\ \frac{6}{11},\ -\ \frac{2}{11}$

d)

$-\ \frac{9}{11},\ \frac{6}{11},\ \ \frac{2}{11}$

31.

$Line\ -\ pas\sin g\ -\ through$
( 4, - 5, - 2) &
( - 1, 5, 3 ) is

a)

$\frac{x-4}{1}\ =\ \frac{y+5}{-\ \ 2}\ =\ \frac{z\ +\ 2}{-\ 1}$

b)

$\frac{x+1}{1}\ =\ \frac{y-5}{\ \ 2}\ =\ \frac{z\ -3}{-\ 1}$

c)

$\frac{x}{-\ 1}\ =\ \frac{y}{\ \ 5}\ =\ \frac{z\ }{3}$

d)

$\frac{x}{4}\ =\ \frac{y}{\ \ -\ 5}\ =\ \frac{z\ }{-\ 2}$

32.

Point\ -\ of\ -\ inter\sec tion

of\ -\ line\ ,\

\frac{x-1}{2}\ =\ \frac{y-2}{\ \ -3}\ =\ \frac{z\ +3}{4}

and plane

2x\ +\ 4y\ -\ z\ +\ 1\ =\ 0

is

a)

$\left(\ -\ \frac{10}{3}\ ,\ \frac{3}{2}\ ,\ -\ \frac{5}{3}\right)$

b)

$\left(\ -\ \frac{10}{3}\ ,\ -\ \frac{3}{2}\ ,\ \ \frac{5}{3}\right)$

c)

$\left(\ \frac{10}{3}\ ,\ \frac{3}{2}\ ,\ -\ \frac{5}{3}\right)$

d)

$\left(\ \ \frac{10}{3}\ ,\ -\ \frac{3}{2}\ ,\ \ \frac{5}{3}\right)$

33.

$Point\ -\ of\ -\ inter\sec tion$
of - line - joining ( 3, 4 , 1) &
( 5, 6 , 1)
and - the
xy - plane - is

a)

( 13, 23, 0)

b)

$\left(\ \frac{13}{5},\ \frac{23}{5},\ 0\right)$

c)

$\left(\ -\ 13,\ 23,\ 0\right)$

d)

$\left(\ -\ \frac{13}{5},\ \frac{23}{5},\ 0\right)$

34.

Direction - ratios - of
two - lines - are
a, b , c and
$\frac{1}{bc}\ ,\ \frac{1}{ca},\ \frac{1}{ab}$

then - lines - are

a)

Perpendicular

b)

Parallel

c)

Coincident

d)

None - of - these

35.

$If\ -\ a\ -\ line\ -\ makes$
$angles\ ,\ \alpha\ ,\ \beta\ ,\ \gamma$
with - coordinate - axes
then

a)

$\cos^2\alpha\ +\ \cos^2\beta\ +\ \cos^2\gamma\ =\ 1$

b)

$\cos^2\alpha\ +\ \cos^2\beta\ -\ \cos^2\gamma\ =\ 1$

c)

$\cos^2\alpha\ -\ \cos^2\beta\ +\ \cos^2\gamma\ =\ 1$

d)

$\cos^2\alpha\ +\ \cos^2\beta\ +\ \cos^2\gamma\ =\ 2$

36.

$If\ -\ a\ -\ line\ -\ makes$

angles\ ,\ \alpha\ ,\ \beta\ ,\ \gamma\ ,\

with-coordinate-axes

then

\sin^2\alpha\ +\sin^2\beta\ +\ \sin^2\gamma\ =

a)

2

b)

1

c)

3

d)

0

37.

$If\ -\ a\ -\ line$
makes
$α,β,γ\$
angles - with
coordinate - axes - then
$\frac{1\ -\ \tan^2\alpha}{1\ +\ \tan^2\alpha}+\frac{1}{\sec2\beta}-\ 2\sin^2\gamma\ =$

a)

- 1

b)

1

c)

- 2

d)

2

38.

A - line - makes

angles,\ \alpha\ ,\ \beta\ ,\ \gamma

with - coordinate - axis

and,\ \alpha+\ \beta\ =\ 90^0,

then\ ,\ \gamma\ =

a)

0

b)

$90^0$

c)

$180^0$

d)

None

39.

If - two - lines

intersect , then,

shortest - distance

between - them - is

a)

0

b)

1

c)

2

d)

None

40.

Equation - of

XOY, plane

is

a)

x = 0

b)

y = 0

c)

z = 0

d)

None

41.

$\frac{x}{a}+\ \frac{y}{b}+\frac{z}{c}\ =\ 1$
is

a)

A - line

b)

A - plane

c)

Both

d)

None

42.

$Two\ -\ Lines\ ,\$
$\frac{x\ -\ x_i}{a_i}\ =\ \frac{y\ -\ y_i}{b_i}=\ \frac{z\ -\ z_i}{c_i}\$
$\left(\ i\ =1,\ 2\right)$
are - perpendicular - then

a)

$a_1a_2+b_1b_2+c_1c_2\ =\ 1$

b)

$a_1a_2+b_1b_2+c_1c_2\ =\ 0$

c)

$a_1a_2+b_1b_2+c_1c_2\ =\ 2$

d)

$a_1a_2+b_1b_2+c_1c_2\ =\ 3$

43.

Direction - ratio - of
line

\frac{x+2}{2}=\ \frac{2y-5}{3},\ z\ =\ -1

are

a)

2 , 3 , 0

b)

4, 3 , 0

c)

1, 3 , 0

d)

2, 3 , -1

44.

Direction - cosines - of
a - line - are

\left(\frac{1}{c},\ \frac{1}{c},\ \frac{1}{c}\right)

then

a)

c = 1

b)

$c\ =\ \pm\ \sqrt{2}$

c)

$c\ =\ \pm\ \sqrt{3}$

d)

c = 0

45.

$Direction\ -\ \cos ine\$
of - a - line
formed - by,
x = 0, and
z = 0, is

a)

1 , 0, 0

b)

0, 1, 0

c)

0, 0 , 1

d)

0, 0 ,0

46.

Which - is - not
a - line

a)

$\frac{x−x_1}{l}=\frac{y−y_{1\ }}{m}=\frac{z−z_1}{n}$

b)

$\frac{x−x_1}{x_2-\ x_1}=\frac{y−y_{1\ }}{y_2-\ y_1}=\frac{z−z_1}{z_2-\ z_1}$

c)

ax + by + cz + d = 0

d)

y = 1

47.

line,\

\frac{x\ -\ a}{p}=\ \frac{y-\ b}{q}\ =\frac{z\ -\ c}{r}

passes - through

a)

( 0, 0 , 0)

b)

( p, q, r)

c)

( a, b , c )

d)

none

48.

Two - planes

intersect -at - a

a)

Plane

b)

Line

c)

circle

d)

None

49.

A - line - can - be

represented

in

a)

vector - form - only

b)

Cartesian - form - only

c)

Vector - and cartesian - form, both

d)

None

50.

$\frac{x\ -\ a}{p}=\ \frac{y-\ b}{q}\ =\frac{z\ -\ c}{r}$
is - line - in

a)

Vector - form

b)

Cartesian - form

c)

None

d)

Both

12 : QUIZ : STRAIGHT LINES: 10 JAN

Total questions: 50

Worksheet time: 25mins

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