Find the angle between force F = (3i +4j -5k) unit and displacement d = (5i +4j -3k) unit. Also find the projection of F on d.

Question

Find the angle between force F = (3i +4j -5k) unit and
displacement d = (5i +4j -3k) unit Also find the projection of F on
d

Kranav Sharma · Accepted Answer

We know that the angle between two vectors is given by $\cos â¡ Î¸ = \frac{\overset{â†’}{F} \overset{â†’}{d}}{F d} H e r e â¢ â€‰ â€‰ \overset{â†’}{F} \overset{â†’}{d} = (3 \hat{â€‰ â€‰ i} + 4 \hat{j} âˆ’ 5 \hat{k}) â€‰ â¢ â€‰ â€‰ (5 \hat{â€‰ â€‰ i} + 4 \hat{j} âˆ’ 3 \hat{k}) = 15 + 16 + 15 = 46 F d = (\sqrt{3^{2} + 4^{2} + {(âˆ’ 5)}^{2}}) â€‰ â€‰ â€‰ (\sqrt{5^{2} + 4^{2} + {(âˆ’ 3)}^{2}}) = (\sqrt{9 + 16 + 25}) \sqrt{(25 + 16 + 9)} = 50 S o, â¢ â€‰ â€‰ \cos â¡ Î¸ â€‰ = \frac{46}{50} = 0 92 Î¸ = {\cos â¡}^{âˆ’ 1} (0 92)$ Projection of F on D is $F â¢ \cos â¡ Î¸ â¢ = \sqrt{50} \cos â¡ â€‰ (23 07) = 6 5 â¢ â€‰ N$