Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Given $a = \hat{i} + 2 \hat{j} - 3 \hat{k}, b = 2 \hat{i} - \hat{j} + \hat{k}$ , and line $L$ defined by $r \times b = a \times b$ .

Find the shortest distance from $P = (0, 1, 2)$ to $L$ .

Answer:

Solution:

$L$ is $r = a + t b$ . Orthogonal projection of $P$ gives $t = 2/3$ and distance $219 /3$ .

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Line ( Equation etc.)

⏱ 2mℹ️ Source: QB

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