Find the unit vector (in xy plane) obtained by rotating j counterclockwisene obtained by rotating j counterclockwise `(3pi)/4` radian about the origin.

Find the unit vector (in xy plane) obtained by rotating j counterclockwisene obtained by rotating j counterclockwise (3 pi)/(4) radian about the origin.

Let a vector a hati + beta hatj be obtained by rotating the vector sqrt3 hati + hatj by an angle 45^(@) about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having vertices (alpha, beta) , (0, beta) and (0,0) is equal to:

Triangle PQR , shown in the diagram above , is translated 4 units to the right and 5 units down. The resulting triangle is then rotated 180^@ counterclockwise about the origin. What is the final image of point P ?

If z = 2 - 2i, find the rotation of z by theta radians in the counter clockwise direction about the origin when theta = (3pi )/(2)

If z = 2 - 2i, find the rotation of z by theta radians in the counter clockwise direction about the origin when theta = (pi)/(3)

If z = 2 - 2i, find the rotation of z by theta radians in the counter clockwise direction about the origin when theta = (2pi)/(3)

For some non zero vector vecv , if the sum of vecv and the vector obtained from vecv by rotating it by an angle 2alpha equals to the vector obtained from vecv by rotating it by alpha then the value of alpha , is