Mathematics - Vector Question with Solution | TestHub

MathematicsVectorVector equation of a line, Vector equation of the angle bisectorsMedium2 minPYQ_2021

MathematicsMediumsingle choice

The equation of the line through the point $(0, 1, 2)$ and perpendicular to the line $\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{- 2}$ is :

Answer:

Solution:

$\frac{x - 1}{2} = \frac{y + 1}{3} = \frac{z - 1}{- 2} = r$

$\Rightarrow P (x, y, z) = (2 r + 1, 3 r - 1, - 2 r + 1)$

Since, $\vec{Q P} ⊥ (2 \hat{i} + 3 \hat{j} - 2 \hat{k})$

$\Rightarrow 4 r + 2 + 9 r - 6 + 4 r + 2 = 0$

$\Rightarrow r = \frac{2}{17}$

$\Rightarrow P (\frac{21}{17}, \frac{- 11}{17}, \frac{13}{17})$

$\Rightarrow \vec{P Q} = \frac{21 \hat{i} - 28 \hat{j} - 21 \hat{k}}{17}$

So, $\vec{Q P} : \frac{x}{- 3} = \frac{y - 1}{4} = \frac{z - 2}{3}$

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

⏱ 2mℹ️ Source: PYQ_2021

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