A drone flies from its base station to point with displacement vector km

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A drone flies from its base station

P

to point

Q

with displacement vector

\mathbf{a}=5\hat{i}+4\hat{j}+2\hat{k}

km. It then flies from

Q

to point

R

with displacement vector

\mathbf{b}=-3\hat{i}+6\hat{j}-\hat{k}

km. (i) Find the vector

\mathbf{c}

representing the direct displacement from

P

R

. Express your answer in component form. (ii) Calculate the scalar product

\mathbf{a}\cdot\mathbf{c}

. (iii) Hence determine, correct to the nearest degree, the angle between

\mathbf{a}

and

\mathbf{c}