Exam 11: Vectors; Lines, Planes, and Quadric Surfaces in Space

The angle, in degrees and correct to two decimal places, between $\mathbf { v } = 2 \mathbf { i } + 3 \mathbf { j } + \mathbf { k }$ and $\mathbf { w } = \mathbf { i } - \mathbf { j } - \mathbf { k }$ is

Which of the following is not true? ​

Let $P _ { 1 } = ( 0,1 , - 4 )$ and $P _ { 2 } = ( - 2,8,0 )$ If v is $\overrightarrow { P _ { 1 } P _ { 2 } }$ in standard position, then v is

The cross product of $\mathbf { v } = 3 \mathbf { i } + \mathbf { j } - \mathbf { k }$ and $\mathbf { w } = - 2 \mathbf { i } - 2 \mathbf { j } + \mathbf { k }$ is

The vector projection of $\mathbf { v } = 0$ onto $\mathbf { w } = 2 \mathbf { i } + \mathbf { j } - 3 \mathbf { k }$ is

Let $P _ { 1 } = ( 6,2,1 )$ and $P _ { 2 } = ( 3,0,2 )$ v is $\overrightarrow { P _ { 1 } P _ { 2 } }$ in standard position, then v is

The distance between the parallel planes $- 4 x + y + z = 4$ and $- 4 x + y + z = - 1$ is

The cross product of $\mathbf { v } = 2 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k }$ and $\mathbf { w } = - \mathbf { i } + \mathbf { j } - 4 \mathbf { k }$ is

Let $\mathbf { u } = \langle 1,1 , - 6 \rangle , \mathbf { v } = \langle 3,0,8 \rangle$ , and $\mathbf { w } = \langle - 3 , - 1,2 \rangle$ Then $\| \mathbf { u } \| + \| \mathbf { v } \| - \| \mathbf { w } \|$ is

Which of the following is not true? ​

Which of the following is not true? ​

The parametric equations of the line of intersection of the planes x + y + z = 1 and x + y = 2 are

The equation of the sphere centered at (1,5,4) and tangent to the xz-plane is

In the three-dimensional Euclidean space, the graph of $3 x ^ { 2 } + 3 y ^ { 2 } = 16$ is

The area of the parallelogram PQRS with vertices $P = ( 1 , - 3,7 ) , Q = ( 2,1,1 )$ and $R = ( 6 , - 1,2 )$ is

In the three-dimensional Euclidean space, the graph of $z ^ { 2 } = x ^ { 2 } + 4 y ^ { 2 }$ is

The area of the parallelogram PQRS with vertices $P = ( - 4,6,3 ) , Q = ( 1,1 , - 5 )$ and $R = ( - 2,4,1 )$ is

In the three-dimensional Euclidean space, the graph of $z = x ^ { 2 } + \frac { y ^ { 2 } } { 4 }$ is

Which of the following is not necessarily true? ​

The volume of the parallelepiped whose adjacent sides are the vectors and $\mathbf { u } = 2 \mathbf { i } + \mathbf { j } - 2 \mathbf { k }$ is