Mathematics - Vector Question with Solution | TestHub

MathematicsVectorVector equation of a line, Vector equation of the angle bisectorsEasy2 minPYQ_2024

MathematicsEasysingle choice

Let $P (3, 2, 3), Q (4, 6, 2)$ and $R (7, 3, 2)$ be the vertices of $∆ PQR$ . Then, the angle $∠ QPR$ is

Answer:

Solution:

Given,

$\Rightarrow \vec{QP} = - \hat{i} - 4 \hat{j} + \hat{k}$ and $\vec{RP} = - 4 \hat{i} - \hat{j} + \hat{k}$

$\cos ∠ QPR = \frac{\vec{QP} \cdot \vec{RP}}{|\vec{QP}| |\vec{RP}|}$

$\Rightarrow \cos ∠ QPR = \frac{4 + 4 + 1}{\sqrt{1 + 16 + 1} \sqrt{16 + 1 + 1}}$

$\Rightarrow \cos ∠ QPR = \frac{9}{18} = \frac{1}{2}$

$\Rightarrow ∠ QPR = \frac{π}{3}$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Vector equation of a line, Vector equation of the angle bisectors

⏱ 2mℹ️ Source: PYQ_2024

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