Question

a vector OA = 3i is rotated by an angle x about its starting point O in x-y plane in clockwise sense, as seen by an observer located at a point on +y axis. the new vector will be​

Answer 1

The Main Answer is: The new vector is 3cosx (i) - 3cosy (j)

Given: Original vector OA = 3 (i)

           It is rotated by an angle 'x' clockwise

To Find: New vector

Solution:

• The given vector OA (3i) lies on the x-axis as it has direction only in (i) which is the direction of the x-axis.

• When rotated clockwise, the new vector will lie in the 4th quadrant.

• Here, the vector will have positive x-direction (i) and negative y-direction (-j).

For OA, when it is rotated by an angle of x clockwise, it forms the angle x with the x-axis.

Let the new vector be = OB

Thus, the components of OB will be:

x- component = 3cosx

y-component = 3sinx

Writing in vector format, i.e., with the directions we previously concluded-

OB = 3cosx (i) + 3sinx(-j)

Therefore, the new vector obtained is 3cosx (i) + 3sinx(-j).

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