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Question

Vector A has a magnitude of 2 units and makes an angle of 30 with the positive x- axis, Vector B has a magnitude of 6 units and makes an angle of 30  with the y- axis(clockwise). Find the magnitude of the resultant of Vector A & -B and also the angle that it makes with Vector A.


  1. Magnitude =     

  2. Magnitude =     

  3. Magnitude =     

  4. Magnitude =     


Solution

The correct option is A

Magnitude =     


Given:

Using parallelogram law 

Now we know magnitude of resultant is give by the formula 

a2+b2+2ab cosθ 

So we have 

22+62+24 cos150=28 

Now we know to find the angle that it makes with the A vector we have the formula 

tanθ=b cosθ(a+b sinθ)

tanθ=6 cos 150(2+6 sin 150)=3(233)

  

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