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1:scalar product of two vectors: (1,2,-2) and (1,-2,2)

2. One of: “If non-zero vectors x and y are perpendicular, then”

“If non-zero vectors x and y are parallel, then”

“If x is a unit vector with same direction and sense as y, then”

a) x = y, b) x = ky for some scalar k, c) x = y / |y|, d) x . y = 0, e) x . y = 1

3. Find cosθ, where θ is the angle between a = (1, 2, 4) and b = (4, –2, 1).

4. Write down a parametric equation of a given straight line.

5. A direction perpendicular to the plane 2x – y + z = 9 is:

a) (2x, –y, z), b) (4, 0, 1), c) (1, 1, –1), d) (2, –1, 1).

6. If the plane 5x + y – 3z = k contains the point (1, 4, 2) then k = ?

7. The line x = (–1, 2, 4) + t(5, 1, 0) meets the plane y = 0 at the point (?, 0, ?).

8. The projection of the vector (4, 0, 7) onto the direction (–1, –2, 2) is ?

9. The distance from the point (1, 2, –5) to the plane 2x + y – 2z = 8 is ?

10. Find the speed of a particle at a given time, given the position vector as a function of time.