3D Geometry 3 Question 58

####58. The unit vector perpendicular to both L1 and L2 is

(a) i^+7j^+7k^99

(b) i^7j^+5k^53

(c) i^+7j^+5k^53

(d) 7i^7j^k^99

Assertion and Reason

For the following questions, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows.

(a) Statement I is true, Statement II is also true; Statement II is the correct explanation of Statement I

(b) Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I

(c) Statement I is true; Statement II is false

(d) Statement I is false; Statement II is true

Show Answer

Answer:

Correct Answer: 58. (b)

Solution:

  1. The equations of given lines in vector form may be written as L1:r=(i^2j^k^)+λ(3i^+j^+2k^)

and L2:r=(2i^2j^+3k^)+μ(i^+2j^+3k^)

Since, the vector is perpendicular to both L1 and L2.

|i^j^k^312123|=i^7j^+5k^

Required unit vector

=(i^7j^+5k^)(1)2+(7)2+(5)2=153(i^7j^+5k^)



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