Question

If the vector A=3i+4j is rotated by an angle 143⁰ in clockwise direction then it becomes Xi-yj then what is the value of x+y

Answer 1

Answer:

X+Y= 5.012 or - 3.414 depending upon direction of your rotation ( clockwise or counterclockwise)

Explanation:

A= 3i+4j

B= xi-yj (say)

|A|=|B| because the direction of A is changed

This gives 25= x^2+y^2 ... (1)

By dot product of A and B, we get

A*B = 3x-4y= |A||B| cos 143°

Cos 143° = - 0.798

Therefore, 3x-4y= 5*5*(-0.798)

3x-3y= - 19.965 ... (2)

By solving (1) and (2) we get,

X=0.012 & Y=5

OR

X= - 4.803 & Y=1.389

And henceforth,

X+Y=5.012

OR

X+Y= - 3.414

I HOPE YOU GOT YOUR ANSWER

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