Vector Summative Assessment Questions

Vector Summative Assessment Questions

Section A

1. Which of the following sets of vectors are co-planar?

(A)

(B)

(C)

(D)

2. Which two points are separated by a distance of exactly 7 units?

(A)

(B)

(C)

(D)

3. Which two vectors have an angle between them of 60°?

(A)

(B)

(C)

(D)

4. For what values k and l does the cross product

(A)

(B)

(C)

(D)

5. Vector . Which of the following is a unit vector in the direction

(A)

(B)

(C)

(D)

Section B

The diagram shows a cube in which the length of each side is 4 units. The unit vectors i, j and k are parallel to respectively. The mid-points of OA and DG are P and Q respectively and R is the centre of the square face ABFE.

Use a scalar product to find angle QPR.

[4]

Section C

The line l has equation r = j + k + s (i – 2 j + k). The plane p has equation .

(i) Show that the line l lies in the plane p.

[2]

(ii) A second plane is perpendicular to the plane p, parallel to the line l and contains the point with position vector 2 i + j +4 k. Find the equation of this plane, giving your answer in the form .

[6]

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