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Angle between (\hat{l}+\hat{j}) and (\hat{l}-\hat{j}) is (in degrees)

 

Option: 1

90


Option: 2

60


Option: 3

45


Option: 4

30


Answers (1)

As we learned

Scalar , Dot or Inner Product -

Scalar product of two vector \vec{A} & \vec{B} written as \vec{A} \cdot \vec{B} is a scalar quantity given by the product of magnitude of \vec{A} & \vec{B} and the cosine of smaller angle between them.

\vec{A}\cdot \vec{B}= A\, B\cdot \cos \Theta

- wherein

showing representation of scalar products of vectors.

 

 \\*(\hat{l}+\hat{j})\cdot (\hat{l}-\hat{j})=\left | \hat{l}+\hat{j} \right |\left | \hat{l}-\hat{j} \right |\cdot \cos \theta \\*\\*Using\; \; \vec{A}\cdot \vec{B}=AB\cos \theta \\*\Rightarrow \cos \theta =\frac{(\hat{l}+\hat{j})\cdot (\hat{l}-\hat{j})}{\left | \hat{l}+\hat{j} \right |\left | \hat{l}-\hat{j} \right |}=\frac{0}{\sqrt{2}\cdot \sqrt{2}}=0\\*\\*\therefore \theta =90^{\circ}

 

Posted by

Kshitij

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