There are two vectors . Vector is inxy plane and of magnitude 5 units and vector isx-z plane and of magnitude units as shown. Theangle between the vectors is . Find n.

JEE MainPhysicsModerateVector

There are two vectors
$\overset{\rightarrow}{OA}\&\overset{\rightarrow}{OB}$ . Vector
$\overset{\rightarrow}{OA}$ is inxy plane and of magnitude 5 units and
vector $\overset{\rightarrow}{OB}$ isx-z plane and of magnitude
$\sqrt{2}$ units as shown. Theangle between the vectors
$\overset{\rightarrow}{OA}\&\overset{\rightarrow}{OB}$ is $\theta = \cos^{- 1}(\frac{3}{n\sqrt{2}})$ .
Find n.

Show answer and solution

\overset{\rightarrow}{OA} = 5cos53^{\circ}\overset{\hat{}}{i} + 5sin53^{\circ}\overset{\hat{}}{j} = 3\overset{\hat{}}{i} + 4\overset{\hat{}}{j}

\overset{\rightarrow}{OB} = \sqrt{2}cos45^{\circ}\overset{\hat{}}{i} + \sqrt{2}sin45^{\circ}\overset{\hat{}}{k} = 1\overset{\hat{}}{i} + 1\overset{\hat{}}{k}

cos\theta = \frac{\overset{\rightarrow}{OA} \cdot \overset{\rightarrow}{OB}}{|\overset{\rightarrow}{OA}||\overset{\rightarrow}{OB}|} = \frac{3 + 0}{5 \cdot \sqrt{2}} = \frac{3}{5\sqrt{2}}

\Rightarrow \theta = \cos^{- 1}(\frac{3}{5\sqrt{2}})

Source: Grass-G / P-18 Physics paper 27 Nov Third.docx

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