Question

A vector ICAP + root 3 J cap rotates about its tail through an angle 60 degrees in clockwise direction then the new vector is

Answer 1

Vector = i + √3 j

Tan θ = y / x
Tanθ = √3
θ = 60°
Angle between vector and x-axis is 60°

If it is rotated clockwise 60° then it will align along x-axis
It’s magnitude will not change.

Therefore,
Initial magnitude of vector = Final magnitude of vector
1^2 + (√3)^2 = x
x = 4

∴ New vector = 4 i

Answer 2

The new vector value is 2Î.

Given,

A vector Î + $\sqrt{3}$$\vec j$

The angle of rotation is 60°.

To Find,

The value of the new vector.

Solution,

Given that a vector Î + $\sqrt{3} \vec j$

From the figure, it is clear that the vector $\vec OA$ is $\vec i +\sqrt{3} \vec j$

Then the vector is rotating in a clockwise direction at an angle of 60°.

The vector is rotating about its tail, so the value of its magnitude is not changing.

| OA | = $\sqrt{1^{2} + \sqrt{3} ^{2} }$

|OA| = $\sqrt{1 + 3}$

|OA| = $\sqrt{4}$

|OA|= 2.

When taking tanФ, here the angle is 60°.

therefore,

tanФ,  = $\frac{y}{x}$

tanФ = $\frac{\sqrt{3} }{1}$

tanФ = $\sqrt{3}$

And the value of Ф is 60°.

When the vector is rotated clockwise it means that the Ф value becomes zero.

So, the new vector will be 2Î.

Hence, 2Î is the new vector.

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