The position vector OP of point P(20, 10) is rotated anti-clockwise

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The position vector OP of point P(20, 10) is rotated anti-clockwise in X-Y plane by an angle θ = 30° a such that point P occupies position Q, as shown in the figure. The coordinates (x, y) of Q are

1. (12.32, 18.66)
2. (18.66, 12.32)
3. (22.32 ,8.26)
4. (13.40, 22.32)

Correct Option: A

Let Co-ordinates of Q are (x', y') and rotation about x-y plane anti clockwise.

X'

=

cosθ

-sinθ

X

Y'

sinθ

cosθ

Y

X'

=

cos30

-sin30

20

Y'

sin30

cos30

10

=		0.866	-0.5				20
		0.5	0.866				10

X'

=

0.866 × 20

-0.5 × 10

=

12.32

Y'

0.5 × 20

0.866 × 10

18.66

(x', y') = (12.32, 18.66)