Question

a vector 3i+4j rotates about its tail through an angle of 53degrees in clockwise direction.then what is the new vector

Answer 1

Explanation:

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Answer 2

The new vector is A$_{1}$ = 5i.

Given:

A vector A = 3i + 4j.

To Find:

The new vector that is formed on rotating A at an angle of 53° in a clockwise direction.

Solution:

We have been given a vector

A = 3i + 4j

Note that since the x-component = 3 and the y-component = 4 are positive,

A lies in the first quadrant.

The magnitude of A is given by A = $\sqrt{x^{2} +y^{2} }$ = $\sqrt{3^{2} +4^{2} }$ = 5.

Let the angle that A makes with the x-axis be θ. It is calculated as;

tanθ = y/x = 4/3

⇒ θ = $tan^{-1}$ (4/3) = 53°.

Hence A makes an angle of 53° with the x-axis.

This vector is rotated about its tail at an angle of 53° in a clockwise direction. Hence the new vector, say A$_{1}$, makes an angle of α = 0° with the x-axis.

A$_{1}$ = Acosαi + Asinαj = 5cos0i + 5sin0j = 5i (as cos0 = 1 and sin0 = 0)

∴ The new vector is A$_{1}$ = 5i.

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