The angle between two vectors :

\overrightarrow{A}=3\hat{i}+4\hat{j}+5\hat{k}  and \overrightarrow{B}=3\hat{i}+4\hat{j}-5\hat{k}   will be

 

  • Option 1)

    0

  • Option 2)

    180\degree

  • Option 3)

    90\degree

  • Option 4)

    45\degree

 

Answers (1)

As we discussed in concept

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.

 

 we know that 

\vec{A}.\vec{B}=AB\cos \theta

=\cos \theta =\frac{\vec{A}.\vec{B}}{AB}

given\ \vec{A}=3\hat{i}+4\hat{J}+5\hat{K}

given\ \vec{B}=3\hat{i}+4\hat{J}-5\hat{K}

(3\hat{i}+4\hat{j}+5\hat{k}).(3\hat{i}+4\hat{j}-5k)=AB\cos \theta

9+0+0+0+16+0+0+0-25=AB\cos \theta

25-25=AB\cos \theta

\cos\theta =0

\theta =90^{\circ}


Option 1)

0

Option is incorrect

Option 2)

180\degree

Option is incorrect

Option 3)

90\degree

Option is correct

Option 4)

45\degree

Option is incorrect

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