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Question

The angle between the two vectors $$-2\hat i+3\hat{j}+\hat{k}$$ and $$\hat i+2\hat {j}-4\hat{k}$$ is:


A
0o
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B
90o
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C
180o
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D
45o
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Solution

The correct option is B 90$$^{o}$$
The angle between the two vectors $$\vec{A}$$ and $$ \vec {B}$$ is 
$$ cos\theta=\dfrac{\vec{A} \cdot \vec{B}}{\left | \vec{A} \vec {B} \right |}$$
 $$\vec{A}  \cdot \vec {B}$$ =  $$(-2i+3\overline{j}+\overline{k}) \cdot (i+2\overline{j}-4\overline{k})= -2+6-4 = 0$$
$$\vec{A} = \sqrt{(2)^2+(3)^2+(1)^2}=\sqrt{14}$$
$$\vec{B} = \sqrt{(1)^2+(2)^2+(4)^2}=\sqrt{21}$$
$$ cos\theta=\dfrac{0}{\sqrt{14}\sqrt{21}}$$ or $$\theta = 90^0$$

Physics

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