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