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The distance of the point having positio...

The distance of the point having position vector `-hat(i) + 2hat(j) + 6hat(k)` from the straight line passing through the point `(2, 3, –4)` and parallel to the vector, `6hat(i) + 3hat(j) -4hat(k)` is:

A

6

B

7

C

8

D

9

Text Solution

Verified by Experts

The correct Answer is:
B

From the figure,
`vec(AP) =-3hati-hatj+10hatk`
`|vec(AP)|=sqrt(100)`
`vec(PN)` is perpendicular to the line.
`vec(AN)` = The projection of `vec(AP)`, on the line, i.e., on `6hati+3hatj-4hatk`
`=|(vec(AP).(6hati+3hatj)-4hatk)/(6hati+3hatj-4hatk)|`
`=|(-18-3-40)/sqrt(60)|=sqrt(61)`
`therefore PN^(2)=AP^(2)-AN^(2)=110-61=49`
`therefore PN=7`
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