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Help me answer: If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

  • Option 1)

    0o

  • Option 2)

    90o

  • Option 3)

    45o

  • Option 4)

    180o

 
Answers (1)
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As we learned in

Triangle law of vector Addition -

If two vector are represented by both magnitude and direction by two sides of triangle taken in same order then their resultant is represented by 3rd side of triangle. 

- wherein

Represents triangle law of vector Addition

 

 \left | \vec{A}-\vec{B} \right |\:=\:\left | \vec{A}+\vec{B} \right |

A^{2}+B^{2}-2ABCos\theta \:=\:A^{2}+B^{2}+2ABCos\theta

4ABCos\theta \:=\:0

Cos\theta\:=\:\frac{0}{4AB}\:=\:0^{\circ}


Option 1)

0o

This option is incorrect.

Option 2)

90o

This option is correct.

Option 3)

45o

This option is incorrect.

Option 4)

180o

This option is incorrect.

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