Question

a vector 4i cap + 3jcap rotate about its tail through 74° in clockwise direction then the new vector is
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Answer 1

Given:

Vector (AB) = 4î + 3j

Angle about which the vector is rotated in clockwise direction = 74°

To find:

The New vector.

Solution:

Since the vector is just rotated therefore its magnitude will remain same.

|AB| = √(4²+3²)

|AB| = 5

The angle that the vector is making with the x axis before rotation is:

tanα = 3/4

α = tan⁻¹3/4 = 36.87°

When the vector is rotated in clockwise direction:

It will make (β = 74°- 36.87° = 37.13°) from the positive x axis .

β is a negative angle as it is below negative axis:

Therefore, the vector = 5î cos(-37.13)° + 5j sin (-37.13)°

=  3.986î - 3.018j

The new vector is 3.986î - 3.018j.

Answer 2

Given : a vector 4i cap + 3jcap rotate about its tail through 74° in clockwise direction

To Find : new vector

Solution:

Vector  4 i  + 3j

Tanθ =  3/4

=> θ = 37°

Vector = Rcosθi + RSinθj

R = √4² + 3²   = 5

=> Vector = 5cos37°i + 5Sin37°j

Rotated 74° in clockwise direction

37°  =  74° = -  37°

New Vector = 5cos(-37°)i + 5Sin(-37°)j

=> New  Vector = 4i - 3j

New  Vector = 4i - 3j

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