The vector A=5i+6j is rotated through an /_45 about the Z axis in the anticlockwise direction. What is the resultant vector?

oopsteekwe 2022-10-16 Answered
The vector A = 5 i + 6 j is rotated through an 45 about the Z axis in the anticlockwise direction. What is the resultant vector?
My attempt: I tried to calculate the resultant vector by using the equation, R = A 2 + B 2 + 2 A B C o s θ
since it is rotated in anticlockwise direction its direction changes. Any hint will be appreciated.
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Answers (2)

Pradellalo
Answered 2022-10-17 Author has 16 answers
HINT
First approach
You can solve it by considering the rotation matrix, where ( x , y ) are the new coordinates after the rotation:
[ x y ] = [ cos ( π 4 ) sin ( π 4 ) sin ( π 4 ) cos ( π 4 ) ] [ 5 6 ]
Second approach
Since A = 5 i + 6 j = ( 5 , 6 ), you can multiply it by exp ( π i 4 )
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Paloma Sanford
Answered 2022-10-18 Author has 3 answers
1) i ( 1 / 2 ) ( i + j )
2) j ( 1 / 2 ) ( i + j )
3) 5 i + 6 j
( 1 / 2 ) ( 1 ) i + ( 1 / 2 ) ( 11 ) j
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