Shape and Space 8

4 marks · Hard

A vector has a magnitude of 13 and makes an angle of with the positive -axis. Prove that the vector could be , giving your reasoning using the definitions of vector magnitude and direction.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

Must show: Calculation and verification of magnitude, Calculation and verification of direction (angle)

Common mistakes: Switching x and y when calculating the angle; Forgetting to use inverse tangent for direction

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Uses to find the magnitude for .

A1 · 1 mark · Shows the magnitude is indeed 13. (follow-through)

M2 · 1 mark · Calculates the angle to the positive x-axis using . (follow-through)

A2 · 1 mark · Shows that the angle is 67.4°, correctly matching the given value. (follow-through)

Worked solution

Firstly, calculate the magnitude of :

So the magnitude is correct.

Next, calculate the angle with the positive x-axis:

Therefore, is a vector of magnitude 13 which makes an angle of 67.4° with the positive x-axis.