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Mathematics - Vector Question with Solution | TestHub

MathematicsVectorDistance of a Point from a LineHard2 minQB

MathematicsHardsingle choice

Passage / Comprehension

Given $\vec a=\hat i+2\hat j-3\hat k$, $\vec b=2\hat i-\hat j+\hat k$, and line $L$ has equation $\vec r\times\vec b=\vec a\times\vec b$.

The shortest distance of the point $P (0, 1, 2)$ from the line L is equal to -

Options:

Answer:

Solution:

The line is $r = a + t b$ . For $P (0, 1, 2)$ , the perpendicular foot occurs at $t = \frac{2}{3}$ , giving $M = (\frac{7}{3}, \frac{4}{3}, - \frac{7}{3})$ . Thus $PM = \frac{219}{9} = \frac{219}{3}$ .

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Distance of a Point from a Line

⏱ 2mℹ️ Source: QB

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