(Three-dimensional displacement) A vector has magnitude

PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane

Problem

(Three-dimensional displacement) A vector

\vec A

has magnitude

20\,\text{N}

. The angle between

\vec A

and the positive

z

-axis is

40^{\circ}

. The projection of

\vec A

on the

x

–

y

plane makes an angle of

30^{\circ}

with the positive

x

-axis. (i) Find the magnitude

A_{xy}

of the projection of

\vec A

on the

x

–

y

plane. (ii) Hence calculate the components

A_x,\,A_y,\,A_z

of the vector. (iii) Verify explicitly that

A_x^2 + A_y^2 + A_z^2

equals

|\vec A|^2

within reasonable rounding error.