Question

find the angle between force f = 2î+ 3 j ^- k^ unit and displacement d = 3i^+ 4j^ + 2 k so find the projection of fand d



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Answer 1

$\sf \vec{F}$ = 2i + 3j - k

$\sf \vec{d}$ = 3i + 4j + 2k

We know that ,

$\sf \vec{F}.\vec{d}=Fdcos\theta\\\\\to \sf cos\theta=\dfrac{\vec{F}.\vec{d}}{Fd}$

$\sf \vec{F}$.$\sf \vec{d}$ = ( 2i + 3j - k ) . ( 3i + 4j + 2k )

⇒ $\sf \vec{F}$.$\sf \vec{d}$ = 6 + 12 - 2

⇒ $\sf \vec{F}$.$\sf \vec{d}$ = 16

Fd = | $\sf \vec{F}$ | | $\sf \vec{d}$ |

⇒ Fd = √(2² + 3² + (-1)²) × √(3² + 4² + 2²)

⇒ Fd = √(4+9+1) × √(9+16+4)

⇒ Fd = √14 × √29

⇒ Fd = 20.15

___________________________

⇒ cosθ = 16 / 20.15

⇒ cosθ = 0.79

⇒ θ = cos⁻¹ (0.79)

⇒ θ = 37.81°

To find projection of F on d ,

Fcosθ = √14 × (0.79) = 2.95 N

Answer 2

Answer:

The projection of F and D is 2.95N.

Learn more:

A vector is defined as a mathematical structure. It has many applications in the field of physics and geometry. We know that the location of the points on the coordinate plane can be represented using the ordered pair such as (x, y). The usage of the vector is very useful in the simplification process of three-dimensional geometry.

Along with the term vector, we have heard the term scalar. A scalar actually represents the real numbers. In simpler words, a vector of n dimensions is an ordered collection of n elements called components.