A unit vector makes an angle of with the positive –axis and equal angles with the…

MATHEMATICS · Multi-part · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

A unit vector

\hat{\mathbf{u}}

makes an angle of

60^{\circ}

with the positive

x

–axis and equal angles with the positive

y

– and

z

–axes. (i) If the direction cosines of

\hat{\mathbf{u}}

are

\ell, m, n

, write the relation connecting

\ell, m, n

. (ii) Using the given information, determine the exact values of

\ell, m

and

n

. (iii) Hence write

\hat{\mathbf{u}}

in component form

\ell\hat{i}+m\hat{j}+n\hat{k}

and check that its magnitude is

1