Is a regular hexagon of side 2 units in the -plane

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

OABCDE

is a regular hexagon of side 2 units in the

XY

-plane.

O

being the origin and

OA

taken along the

X

-axis. A point

P

is taken on a line parallel to

Z

-axis through the centre of the hexagon at a distance of 3 units from

O

. Then, the vector

\mathbf{AP}

is (1)

-\hat{i} + 3\hat{j} + \sqrt{5}\hat{k}

(2)

\hat{i} - \sqrt{3}\hat{j} + 5\hat{k}

(3)

-\hat{i} + \sqrt{3}\hat{j} + \sqrt{5}\hat{k}

(4)

\hat{i} + \sqrt{3}\hat{j} + \sqrt{5}\hat{k}