Question

Find the angle between force (3i+4j-5k)N and displacement (5i+4j-3k)m

Answer 1

Answer:-

$\red{ \boxed{\boxed{ \green{ \bf{ \theta = {cos}^{ - 1} \bigg( \frac{8}{25} \bigg)}}}}}$

Explanation:-

To find:-

Angle between force and displacement.

Solution:-

Given:-

f =( 3i + 4j - 5k )N

d= ( 5i + 4j - 3k) m

we know that ,

Angle between two vector is →

$\bf{cos \: \theta = \frac{ \vec{f}. \vec{d}}{fd} }$

$\bf{ \vec{f}. \vec{d} = (3i + 4j - 5k).(5i + 4j - 3k)} \\ \\ \: \: \: \: \: \: \: \: = 15 + 16 - 15 = 16 \\ \\ \\ \bf{fd = \big( \sqrt{ {3}^{2} + {4}^{2} + {5}^{2} } \big) \big( \sqrt{ {5}^{2} + {4}^{2} + {3}^{2} } \big) }\\ \\ \: \: \: \: \: \: = \sqrt{50}. \sqrt{50} = 50$

Hence,

$\bf{cos \: \theta = \frac{16}{50} } \\ \\ \bf{ cos \: \theta \: = \frac{8}{25} } \\ \\ \boxed{ \red{\theta = {cos}^{ - 1} \bigg( \frac{8}{25} \bigg)}}$