# If $\overrightarrow{A}= 5 \hat i +7 \hat j - 3 \hat k$ and $\overrightarrow{B}=2\hat i +2 \hat {j} +8 \hat {k}$ the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

$\begin{array}{1 1}(A)\;45^{\circ} \\(B)\;60^{\circ} \\(C)\;0^{\circ}\\(D)\;90^{\circ} \end{array}$

## 1 Answer

$\cos \theta = \large\frac{\overrightarrow{A}.\overrightarrow{B}}{|\overrightarrow{A}||\overrightarrow{B}|}$
$\qquad= \large\frac{(5\hat{i}+7 \hat j -3 \hat k ).(2 \hat i +2 \hat j + 8 \hat k)}{|5 \hat i +7 \hat j -3 \hat k ||2 \hat i + 2 \hat j -8 \hat k |}$
$\qquad= \large\frac{(10+14-24)}{(\sqrt {83})( \sqrt {72})}$$=0$
Hence C is the correct answer.
answered Jul 16, 2014 by

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