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
B
90o
C
180o
D
45o

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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