Question

find the angle between force F = ( 3i + 4j - 5k ) unit and displacement d = ( 5i + 4j + 3k ) unit and also find the projection of F and D​

Answer 1

$\huge\mathrm\blue{Answer}$

Refer the attachment

Answer 2

The angle between F and D is 71.3° and projection of F on D is 2.26

Given:

Two vectors F = 3i + 4j - 5k and D =  5i + 4j + 3k

To Find:

Angle between two vectors and projection of F on D

Solution:

The two vectors are F =  3i + 4j - 5k and D = 5i + 4j + 3k

CosФ = $\frac{F.D}{FD}$

cosФ = $\frac{ (3i + 4j - 5k ).(5i + 4j + 3k) }{\sqrt{ 3^{2} +4^{2}+5^{2} }.\sqrt{5^{2}+4^{2}+3^{2} } }$

cosФ = $\frac{15+16-16}{\sqrt{50}.\sqrt{50} }$

cosФ = $\frac{16}{50}$

Ф = 71.2°

Now projection of F on D = $\frac{F.D}{D}$ = $\frac{16}{\sqrt{50} }=2.26$

Hence, the angle between two vectors is 71.2° and projection is 2.26.

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