Free Printable Vector Algebra

1.

If

\overrightarrow{a}\overrightarrow{,b,}\overrightarrow{c}

are three unit vectors such that

\overrightarrow{a}

is perpendicular to

\overrightarrow{b}

, and is parallel to

\overrightarrow{c}

then

\overrightarrow{a}\left(\overrightarrow{b}\times\overrightarrow{c}\right)

is equal to

a)

$\overrightarrow{a}$

b)

$\overrightarrow{b}$

c)

$\overrightarrow{c}$

d)

$\overrightarrow{0}$

2.

$\left[\overrightarrow{a}\overrightarrow{,b}\overrightarrow{,c}\right]=1\$ then the value of $\ \frac{\overrightarrow{a}\cdot\left(\overrightarrow{b}\times\overrightarrow{c}\right)}{\left(\overrightarrow{c}\times\overrightarrow{a}\right)\cdot\overrightarrow{b}}\ +\frac{\overrightarrow{b}\cdot\left(\overrightarrow{c}\times\overrightarrow{a}\right)}{\left(\overrightarrow{a}\times\overrightarrow{b}\right)\cdot\overrightarrow{c}}+\frac{\overrightarrow{c}\cdot\left(\overrightarrow{a}\times\overrightarrow{b}\right)}{\left(\overrightarrow{c}\times\overrightarrow{b}\right)\cdot\overrightarrow{a}}$

a)

-1

b)

2

c)

1

d)

3

3.

If $\ \overrightarrow{a}\ and\ \overrightarrow{b}\$ are the unit vectors such that $\left[\overrightarrow{a},\overrightarrow{b},\ \overrightarrow{a}\times\overrightarrow{b}\right]=\frac{\pi}{4},\$ then the angle between $\ \overrightarrow{a}\ and\ \overrightarrow{b}\$ is

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{2}$

4.

Consider the vectors $\ \overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}$ such that $\ \left(\overrightarrow{a}\times\overrightarrow{b}\right)\times\left(\overrightarrow{c}\times\overrightarrow{d}\right)=\overrightarrow{0}.$ Let $P_1$ and $P_2$ be the planes determined by the pairs of vectors $\overrightarrow{a},\overrightarrow{b}\ and\ \overrightarrow{c},\overrightarrow{d}\$ respectively .Then the angle between $P_1\ and\ P_2\ is\$

a)

$60\degree$

b)

$0\degree$

c)

$90\degree$

d)

$45\degree$

5.

If $\ \overrightarrow{a}\times\left(\overrightarrow{b}\times\overrightarrow{c}\right)=\left(\overrightarrow{a}\times\overrightarrow{b}\right)\times\overrightarrow{c},$ $\ where\ \overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\$ are any three vectors such that $\overrightarrow{b}\cdot\overrightarrow{c}\ne0\ and\ \overrightarrow{a}\cdot\overrightarrow{b}\ne0,\ then\ \overrightarrow{a}\ and\ \overrightarrow{b\ }\ are\$

a)

$inclined\ at\ an\ angle\ \frac{\pi}{3}$

b)

$parallel$

c)

$inclined\ at\ an\ angle\ \frac{\pi}{6}$

d)

$perpendicular\$

6.

If $\ \overrightarrow{a},\ \overrightarrow{b},\overrightarrow{c}\$ are non - coplanar ,non-zero vectors such that $\ \left[\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\right]=3\ then\ \left\{\left[\overrightarrow{a}\times\overrightarrow{b},\ \overrightarrow{b}\times\overrightarrow{c},\overrightarrow{c}\times\overrightarrow{a}\right]\right\}^2\$ is equal to

(a)

7.

If the volume of the parallelpiped with $\ \left(\overrightarrow{a}\times\overrightarrow{b}\right)\times\left(\overrightarrow{b}\times\overrightarrow{c}\right),\left(\overrightarrow{b}\times\overrightarrow{c}\right)\times\left(\overrightarrow{c}\times\overrightarrow{a}\right)\ and\$ $\ \left(\overrightarrow{c}\times\overrightarrow{a}\right)\times\left(\overrightarrow{a}\times\overrightarrow{b}\right)$ as conterminous edges is ,

(a)

8.

If the length of the perpendicular form from the origin to the plane $2x+3y+\lambda z=1,\ \lambda>0\ is\ \frac{1}{5},\$ $then\ the\ value\ of\ \lambda\ is\$

a)

$3\sqrt{2}$

b)

$0$

c)

$1$

d)

$2\sqrt{3}$

9.

The distance between the planes $x+2y+3z+7=0\ \$ and $2x+4y+6z+7=0$ is

a)

$\frac{\sqrt{7}}{2}$

b)

$\frac{\sqrt{7}}{2\sqrt{2}}$

c)

$\frac{7}{2\sqrt{2}}$

d)

$\frac{7}{2}$

10.

If the line $\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+2}{2}$ lines in the plane

$x+3y-\alpha z+\beta=0,$ then $\left(\alpha,\beta\right)$ is

a)

(-6,7)

b)

(-5,5)

c)

(7,-6)

d)

(5,-5)

Vector Algebra

Total questions: 10

Worksheet time: 6mins

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