Forces and act along the directions of the vectors and

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

Forces

\mathbf{F}_1

and

\mathbf{F}_2

act along the directions of the vectors

\mathbf{m}=4\mathbf{i}-\mathbf{j}+3\mathbf{k}

and

\mathbf{n}=-2\mathbf{i}+5\mathbf{j}+\mathbf{k}

, respectively. (i) Determine all unit vectors that are perpendicular to both

\mathbf{m}

and

\mathbf{n}

. (ii) A third force

\mathbf{F}_3

has magnitude

10\,\text{N}

and acts along one of the directions obtained in part (i). Write

\mathbf{F}_3

in component form. (iii) Find the angle between

\mathbf{F}_3

and the resultant force

\mathbf{F}_1+\mathbf{F}_2