Find The Scalar And Vector Projections Of B Onto A

Determine the scalar and vector projection of a to b.

Determine scalar and vector projections from b to a.

a = (4.3)

b = (8.0)

Compatible?

Plan?

The scalar (or component) of b is above a.

comp_a (b) = aà ˆ ™ b / || To || = (4 (8) + (3) (0)) /  ° (4² + 3²) = 32/5

The projection from b to a is just a scalar component multiplied by the unit vector in one direction.

proj_a (b) = aà ˆ ™ b / || To || ² a = (32/25) (4, 3) = (128/25, 96/25)

B to A scalar projection

Vector a = 4i3j

Vector b = 8i 0j

(Vector B) Point UCT (Vector A) = 32 0 = 32 Units .............. (i)

Plural a = square (4 2 + 3 2) = 5

Unit vector a = (vector a) / dimension a = (4/5) i (3/5) j .............. (ii)

b to a = 32 {(4/5) i (3/5) j is a projection.

= (128/5) i (96/5) j .................................... Res

| A X B | = | To || B | sinΘ = 12 = 18sinؘ sinΘ = 2/3 cosؘ = ± ˆš (14/9) = ± ˆš5 / 3 A point B = | To || B | cosΘ = ± 12  5/3 = ± 4  5

Find The Scalar And Vector Projections Of B Onto A