The perpendicular distance of point ( 2 , 0 , - 3 ) from line which passes through the point ( 0 , 2 , - 4 ) and perpendicular to the lines r = ( - 3 i + 2 k ) + ( 2 i + 3 j + 5 k ) , r = ( i - 2 j + k ) + ( - i + 3 j + 2 k ) , where R is

Question

The perpendicular distance of point $(2, 0, - 3)$ from line which passes through the point $(0, 2, - 4)$ and perpendicular to the lines $\vec{r} = (- 3 \hat{i} + 2 \hat{k}) + λ (2 \hat{i} + 3 \hat{j} + 5 \hat{k}),$ $\vec{r} = (\hat{i} - 2 \hat{j} + \hat{k}) + μ (- \hat{i} + 3 \hat{j} + 2 \hat{k})$ , where $λ$ , $μ \in R$ is

Smart Achievers · Accepted Answer

(2)

<img alt="" src="https://smartachievers.online/public/jadv26/125.jpg" />

Solution

1 $\frac{\sqrt{219}}{3}$

2 $\frac{\sqrt{78}}{3}$

3 $\frac{\sqrt{52}}{3}$

4 $\frac{\sqrt{126}}{3}$

Ans.
(2)

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Solution

Q. The perpendicular distance of point (2,0,-3) from line which passes through the point (0,2,-4) and perpendicular to the lines r→=(-3i^+2k^)+λ(2i^+3j^+5k^), r→=(i^-2j^+k^)+μ(-i^+3j^+2k^), where λ, μ∈R is

1 2193

2 783

3 523

4 1263