Free Printable Chapter 10. Three-Dimensional Vectors (Con't)

1.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find the dot product of a.b.

(a)

2.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find the angle between a and b. (round it to the nearest thousandth degree)

(a)

3.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find the dot product of b.a

(a)

4.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Selects all that apply about magnitude a or b.

a)

|a|= √66

b)

|b| = 4

c)

|a| = √32

d)

|b| = 38

e)

|a| = 66

5.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find p, scalar projection of vector a on b. (round it to nearest hundredth)

(a)

6.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find $\overrightarrow{p}$ , vector projection of vector a on b.

a)

$\overrightarrow{p}=2.345i-0.671j-1.364k$

b)

$\overrightarrow{p}=2.368i-0.974j-1.124k$

c)

$\overrightarrow{p}=2.368i-0.947j-1.421k$

d)

$\overrightarrow{p}=4.368i-0.974j-1.124k$

7.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find cross product of these two vectors, $\overrightarrow{a}\times\overrightarrow{b}$

a)

-25i - 31j - 23k

b)

-26i - 32j - 22k

c)

-26i + 32j + 23k

d)

26i + 32j - 22k

8.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find cross product of these two vectors, $\overrightarrow{b}\times\overrightarrow{a}$

a)

25i + 31j + 23k

b)

26i + 32j + 22k

c)

26i + 31j + 23k

d)

-26i - 32j + 22k

9.

Given vector a and b respectively, $\overrightarrow{a}=i+4j-7k$ and $\overrightarrow{b}=5i-2j-3k$ . The vectors are placed tail to tail.

Find the area of parallelogram formed by these two vectors. (round it to the nearest thousandth unit-square)

(a)

10.

Consider vector a and b, $\overrightarrow{a}=2i+5j-3k$ and $\overrightarrow{b}=7i-4j-2k$
. Select one that apply.

a)

vector a and vector b are parallel to each other,

b)

vector a and vector b are perpendicular to each other

c)

vector a and vector b form a certain value of angle between 0 to 90 degrees

d)

vector a and vector b form a certain value of angle between 90 to 180 degrees.

11.

Consider vector a and b, $\overrightarrow{a}=-3i+6j-12k$ and $\overrightarrow{b}=5i-10j+20k$
. Select one that apply.

a)

vector a and vector b are parallel to each other,

b)

vector a and vector b are perpendicular to each other

c)

vector a and vector b form a certain value of angle between 0 to 90 degrees

d)

vector a and vector b form a certain value of angle between 90 to 180 degrees.

12.

Consider vector a, $\overrightarrow{a}=5i+3j+7k$ . Find the direction angles for vector a.

a)

$\alpha=56.713\degree,\ \beta=39.794\degree,\ \gamma=70.774\degree$

b)

$\alpha=56.714\degree,\ \beta=70.774\degree,\ \gamma=39.794\degree$

c)

$\alpha=59.714\degree,\ \beta=36.794\degree,\ \gamma=70.774\degree$

d)

$\alpha=36.794\degree,\ \beta=59.714\degree,\ \gamma=70.774\degree$

13.

If a vector has $\alpha=152\degree\$ and $\beta=73\degree$ , find $\cos^2\gamma$ . (round it to the nearest thousandth)

(a)

14.

Find the equation of the plane containing the point (3, 5, 7) with normal vector $\overrightarrow{n}=11i+2j+13k$

a)

$\left(3+\frac{11}{\sqrt{294}}d\right)i$ + $\left(5+\frac{2}{\sqrt{294}}d\right)j$ + $\left(7+\frac{13}{\sqrt{294}}d\right)k$

b)

11x + 2y + 13z = 134

c)

3x + 5y + 7z = 134

d)

none of answers are correct

15.

Find a vector $\overrightarrow{n}$ normal to the plane 7x - 3y + 8z = 51 $.$

a)

$\overrightarrow{n}=\frac{7}{\sqrt{122}}i$ $-\frac{3}{\sqrt{122}}j$ $+\frac{8}{\sqrt{122}}k$

b)

$\overrightarrow{n}=7i+3j+8k$

c)

$\overrightarrow{n}=-7i+3j-8k$

d)

can't be solved because lack of information

16.

A line containing the point (5, 3, -1) has direction cosines $c_1=\frac{6}{11}\ \ \ c_2=\frac{-2}{11}\ and\ \ \ c_3=\frac{9}{11}$ . Find the particular equation of the line.

a)

$\overrightarrow{r}=\left(5+\frac{6}{11}d\right)i$ + $\left(3-\frac{2}{11}d\right)j$ + $\left(-1+\frac{9}{11}d\right)k$

b)

$\overrightarrow{r}=\left(5d\right)i+\left(3d\right)j-1dk$

c)

$\overrightarrow{r}=\left(\frac{61}{11}d\right)i$ $+\left(\frac{31}{11}d\right)j$ $+\left(\frac{2}{11}d\right)k$

d)

$\overrightarrow{r}=\left(\frac{6}{11}d\right)i$ $+\left(-\frac{2}{11}d\right)j$ $+\left(\frac{9}{11}d\right)k$

e)

No right answers

17.

A line containing the point (5, 3, -1) has direction cosines $c_1=\frac{6}{11}\ \ \ c_2=\frac{-2}{11}\ and\ \ \ c_3=\frac{9}{11}$ . Find the point where the line intersects the plane 7x + 4y - 2z = 39.

a)

$\overrightarrow{r}=1.25i+4.25j+6.625k$

b)

$\overrightarrow{r}=1.25i+4.25j-6.625k$

c)

$\overrightarrow{r}=1.25i-4.25j+6.625k$

d)

$\overrightarrow{r}=-1.25i+4.25j-6.625k$

e)

No right answers

Chapter 10. Three-Dimensional Vectors (Con't)

Total questions: 17

Worksheet time: 1hrs 25mins

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