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Question

If 1,-2,-2 and 0,2,1 are direction ratios of two lines, then the direction cosines of a perpendicular to both the lines are


A

13,-13,23

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B

23,-13,23

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C

-23,-13,23

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D

214,-114,314

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Solution

The correct option is B

23,-13,23


Explanation for correct option:

Step-1: Finding the vector which is perpendicular on two given lines.

Given, direction ratio of the lines are 1,-2,-2 and 0,2,1.

We know that a Vector which is perpendicular to the lines which have direction ratio are a1,b1,c1&a2,b2,c2 is i^j^k^a1b1c1a2b2c2

Vector Which is perpendicular to the lines whose direction ratio are 1,-2,-2 and 0,2,1.is i^j^k^1-2-2021

=2i^-j^+2k^

Step-2: Finding direction cosine.

We know that the direction cosine of a vector ai^+bj^+ck^ is aa2+b2+c2,ba2+b2+c2,ca2+b2+c2

Therefore required direction ratio is 222+-12+22,-122+-12+22,222+-12+22

23,-13,23

Hence, correct answer is option B


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