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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)

best_answer

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

Posted by

prateek

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