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Offline Centres

$P (0, 3, - 2); Q (3, 7, - 1)$ and $R (1, - 3, 1)$ are 3 given points. Let $L_{1}$ be the line passing through P and Q and $L_{2}$ be the line through R and parallel to the vector $\vec{V} = \hat{i} + \hat{k}$

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Perpendicular distance of P from L₂

Shortest distance between L₁and L₂

Area of the triangle PQR

Distance from (0,0,0) to the plane PQR

answer is A, .

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Detailed Solution

A) Take any point on L₂ and find the parameter toget the perpendicular distance

$В) [\begin{array}{lll} \bar{c} - \bar{a} \bar{b} \bar{d} \end{array}]$

$C) \frac{1}{2} | \bar{P} Q \times \bar{P} R |$

$D) |\begin{array}{ccc} x - x_{1} & y - y_{1} & z - z_{1} \\ x_{2} - x_{1} & y_{2} - y_{1} & z_{2} - z_{1} \\ x_{3} - x_{1} & y_{3} - y_{1} & z_{3} - z_{1} \end{array}| = 0$

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