Quiz about Vectors

Question 1

The cross product of vectors A and B is

Accepted Answer

perpendicular to both A and B

Answer

parallel to either A or B

Answer

parallel to both A and B

Answer

perpendicular to either A or B

Question 2

If the dot product of two vectors is equal to zero, then what do we know about the two vectors?

Accepted Answer

They are perpendicular.

Answer

They are parallel.

Answer

They are unit vectors.

Answer

They are both zero vectors.

Question 3

How do you know that two vectors are parallel?

Accepted Answer

Their vector product is 0.

Answer

Their sum is 0.

Answer

Their scalar product is 0.

Question 4

The vector equation of the line through the point (2, -1,0) parallel to the line $$r=<2,1,4>+\lambda<5,1,2>$$

Accepted Answer

$$r=<2,-1,0>+\lambda<5,1,2>$$

Answer

$$r=<2,-1,0>+\lambda<2,1,4>$$

Answer

$$r=<2,1,4>+\lambda<2,-1,0>$$

Answer

$$r=<5,1,2>+\lambda<2,-1,0>$$

Question 5

The cartesian equation of the line $$\left(r=<2,1,3>+\lambda<-1,0,2\right)$$ is:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

The vector equation of the line through the points A(-1, 2, 3) and B(2, 1, 4) is

Accepted Answer

$$r=<-1,2,3>+\lambda<3,-1,1>$$

Answer

$$r=<2,1,4>+\lambda<-1,2,3>$$

Answer

$$r=<-1,2,3>+\lambda<2,1,4>$$

Answer

$$r=<-1,2,3>+\lambda<1,3,7>$$

Question 7

The vector equation of the line $$\frac{x-2}{3}=\frac{y}{2}=z+1\ $$ is

Accepted Answer

$$r=<2,0,-1>+\lambda<3,2,1>$$

Answer

$$r=<3,2,1>+\lambda<2,0,-1>$$

Answer

$$r=<2,0,-1>+\lambda<3,2,0>$$

Answer

$$r=<3,2,0>+\lambda<2,0,-1>$$

Question 8

The value of $$<-1,2,-3>.<2,1,0>$$ is

Accepted Answer

0

Answer

1

Answer

-1

Answer

4

Question 9

The angle between the lines $$r=<2,1,0>+\lambda<3,-1,2>$$ and $$r=<4,1,-2>+\mu<2,0,-1>$$ is

Accepted Answer

$$61.4\degree$$

Answer

$$28.6\degree$$

Answer

$$42.3\degree$$

Answer

$$62.1\degree$$

Question 10

The angle between the lines $$\frac{x-1}{2}=\frac{y+3}{4}=\frac{2-z}{3}$$ and $$\frac{x}{4}=\frac{y+2}{3}=z-2$$ is

Accepted Answer

$$51.7\degree$$

Answer

$$19.1\degree$$

Answer

$$33.1\degree$$

Answer

$$100.9\degree$$

Question 11

In the equation of a plane given by: 3x + 5y + 2z - 13 = 0,

which vector below would be a normal to the plane?

Accepted Answer

[3, 5, 2]

Answer

[3, 0, -2]

Answer

[5, 2, -13]

Answer

[3, -5, 2]

Question 12

If a line is found to be perpendicular to two planes, then the two planes are said to be _____________ .

Accepted Answer

parallel to each other

Answer

orthogonal to each other

Answer

no relationship at all

Question 13

Given plane $$\pi_1$$ passes through point A $$\left(8,-8,4\right)$$ and is parallel to the plane $$\pi_2$$ with the quation $$-2x-y+z=1$$ . Choose the correct statement(s) from this information.

Accepted Answer

Position vector is $$<8,-8,4>$$

Accepted Answer

Normal vector for $$\pi_1$$ is $$<-2,-1,1>$$

Accepted Answer

Equation for $$\pi_1$$ is $$-2x-y+z=-4$$

Answer

Equation for $$\pi_1$$ is $$r.\left(-2i-j+k\right)=4$$

Question 14

The acute angle between the line $$r=2i-j-3k\ +\lambda\left(i-2k\right)$$ and the plane $$r\cdot\left(5i+j-3k\right)=4$$

is

Accepted Answer

$$56.3\degree$$

Answer

$$33.7\degree$$

Answer

$$35.6\degree$$

Answer

$$54.4\degree$$

Question 15

Given two lines L₁ and L₂ as r₁=a₁+tb₁ and r₂=a₂+tb_{2, it is CORRECT to say:}

Accepted Answer

They are parallel if b₁=kb₂

Accepted Answer

They are coincident (equal) if they are parallel and have a common point

Accepted Answer

They are skew if they are not parallel and have no solution for r₁=r₂

Answer

They are skew if they are parallel and have no solution for r₁=r₂

Question 16

Write the vector from A to D

Accepted Answer

a + b

Answer

-a + b

Answer

b - a

Answer

a - b

Question 17

Find an equation for a plane that passes through $$\left(4,6,-9\right)$$ and is parallel to the plane with the equation $$3x+5y+z=6$$

Accepted Answer

$$3x+5y+z=33$$

Answer

$$4x+6y-9z=6$$

Answer

$$4x+6y-9z=33$$

Answer

$$3x-5y+z=33$$

Question 18

Which of the following represents the parametric equations of a line in three-dimensional space?

Accepted Answer

$$x=x_o\ +\ at,\ \ y=y_o\ +\ bt,\ \ z=z_o\ +\ ct,\ $$

Answer

$$\overrightarrow{r}=\overrightarrow{r_o}\ +t\overrightarrow{v}$$

Answer

$$\frac{x-x_o}{a}=\frac{y-y_o}{b}=\frac{z-z_o}{c}$$

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