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Determine the projection of u=1.6i+3.3j in the v=-2.1-.5j direction.

A.8i+.2j

B.2.3i+.5j

C. -.6i-1.3j

D. -1.2i-1.1j

Sagot :

abidemiokin

Answer:

[tex]0.80i +0.2j[/tex]

Step-by-step explanation:

The projection of u on v is expressed as;

[tex]proj_{v} u = \dfrac{u*v}{|v|^2} * v[/tex]

Given

u=1.6i+3.3j

v=-2.1i-.5j

u*v = (1.6i+3.3j )*(-2.1i-0.5j )

u*v = 1.6i(-2.1i) + 3.3j(-0.5j)

u*v = -3.36 - 1.65

u*v = -5.01

|v|² = (√(-2.1)²+(-0.5)²)²

|v|² = (-2.1)²+(-0.5)²

|v|² = 4.41+0.25

|v|² = 4.66

Substitute into the formula;

[tex]= \frac{1.71}{-5.01} * (-2.1i - 0.5j)\\= -0.3413 (-2.1i - 0.5j)\\= 0.8i + 0.17j\\= 0.80i +0.2j[/tex]

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