Question

(a) Under what condition will the equality : |vector A x vector B| = vector A x vector B hold good ?
(b) Two forces 5 N and 7 N are acting at a point. The angle between them is 60°. Find
the resultant force.​

Answer 1

(a) $\large\rm { \:\:\:\:\:\:\:\:\:\: \vec{A} \times \vec { B} = \vec{A} \cdot \vec{B}}$

$\large\rm { \: }$

$\large\rm { \:\:\:\:\:\:\:\:\:\: |A||B| \sin \theta = |A||B| \cos \theta}$

$\large\rm { \: }$

$\large\rm { \:\:\:\:\:\:\:\:\:\: \cancel{|A||B|} \sin \theta = \cancel{ |A||B|} \cos \theta}$

$\large\rm { \ }$

$\large\rm { \:\:\:\:\:\:\:\:\:\: \tan \theta = 1}$

$\large\rm { \ }$

$\large\rm { \:\:\:\:\:\:\:\:\:\: \boxed{ \theta = 45^{\circ}}}$

$\large\rm { \: }$

if angle between vectors $\large\rm { \vec{A}}$ and $\large\rm { \vec{B}}$ is 45°, then this equality holds good.

(b) $\large\rm { F = \sqrt{ 5^{2} + 7^{2} + 2(5)(7) \ \cos 60}}$

$\large\rm { \ }$

$\large\rm { F = \sqrt{25+49+35}}$

$\large\rm { \ }$

$\large\rm { F = \sqrt{109}}$

$\large\boxed{\rm { F = 10.44 N }}$