3.25: Vectors from magnitude and direction

0606/23/O/N/21 — Question 7 · 8 marks

The vector

\mathbf{p}

has magnitude

39

and is in the direction

-5\mathbf{i} + 12\mathbf{j}

. The vector

\mathbf{q}

has magnitude

34

and is in the direction

15\mathbf{i} - 8\mathbf{j}

.

(a)

Write both

\mathbf{p}

and

\mathbf{q}

in terms of

\mathbf{i}

and

\mathbf{j}

.

[4]

(b)

Find the magnitude of

\mathbf{p} + \mathbf{q}

and the angle this vector makes with the positive

x

-axis.

[4]