A vector lies in the -plane

MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors

Problem

A vector

\mathbf{P}=5\,\mathbf{\hat{i}}-12\,\mathbf{\hat{j}}

lies in the

xy

-plane. Which option gives both the unit vector along

\mathbf{P}

and the angle (in degrees) that

\mathbf{P}

makes with the positive

x

-axis? (a)

0.923\,\hat{\mathbf{i}}-0.385\,\hat{\mathbf{j}};\;-67.4^{\circ}

(b)

0.385\,\hat{\mathbf{i}}-0.923\,\hat{\mathbf{j}};\;-67.4^{\circ}

(c)

5\,\hat{\mathbf{i}}-12\,\hat{\mathbf{j}};\;22.6^{\circ}

(d)

0.385\,\hat{\mathbf{i}}-0.923\,\hat{\mathbf{j}};\;67.4^{\circ}