Vector, Line and Plane

Given points A(3, 2, -4) and B(2, 1, -1), so the vector AB is

• 5 + 3j -5k

• -i -3j +3k

• i +j -3k

• -i -j +3k

Given the vector v = 3i -2j +6 k, the magnitude of a is:

• 36

• 49

• 7

• 6

Given the line L: r = a + tb, where a = i+2j+3k and b= 2i -3j + k

• a line with direction vector 2i +4j + 6k is parallel to L

• a line with direction vector 4i -6j + 2k is parallel to L

• a line with direction vector 3i - j + 7k is parallel to L

• a line with direction vector 3i + j - 3k is parallel to L

The scalar product of u and v is zero, therefore...

• vectors u and v are parallel

• vectors u and v are perpendicular

• vectors u and v are equal

• vectors u and v are colinear

Given two lines L₁ and L₂ as r₁=a₁+tb₁ and r₂=a₂+tb_2, it is CORRECT to say

• They are parallel if b₁=kb₂

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

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

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

Which of the following pictures represent the sum A + B ?

• 
• 
• 

Calculate the cross product of <1, -2, 1> and <2, -1, 1>

• <-1, -1, 3>

• 5

• <3, 1, -3>

• <-1, 1, 3>

Which of the following is the difference of vector black and vector red (black - red).

• green

• purple

• blue

• orange

Determine whether the points P (2, 0, 0) and Q (1, 1, 1) lie on the plane 2x − 5y + 3z = 4.

• P is on the plane;

  Q is not.

• Q is on the plane;

  P is not.

• P and Q are both on the plane.

• Neither P nor Q are on the plane.

Determine the Cartesian equation of the plane passing through the point (2, 3, 1) and which has normal vector <2, 0, -1>.

• 2x + 3y + z = 3

• 2x - z = 3

• 3y + 2z = 5

• 2x + z = 1