Physics, asked by sarmapranjit567, 23 days ago

5. The vector A=5i+6j is rotated through an angle 45degree the z-axis in the anticlockwise direction. The resultant vector is​

Answers

Answered by sneharani4184
0

Explanation:

The vector and rotation are both in the x-y plane. So a rotation about the z-axis is the same as a rotation about the origin in the x-y plane.

The matrix for rotation through an angle θ in the plane is

[cos θ -sin θ]

[sin θ cos θ ]

So the resultant vector is

[cos 45 -sin 45][5]

[sin 45 cos 45 ][6]

= (1/sqrt 2)[1 -1][5]

………………. [1 ….1][6]

= (1/sqrt 2)[-1]

…………………[11]

= (-1/sqrt 2, 11/sqrt 2)

= approx. (- 0.7071, 7.7782)

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