Vectors 4 Question 5

5. The unit vector which is orthogonal to the vector 3i^+2j^+6k^ and is coplanar with the vectors 2i^+j^+k^ and i^j^+k^ is

(2004, 1M)

(a) 2i^6j^+k^41

(b) 2i^3j^13

(c) 3j^k^10

(d) 4i^+3j^3k^34

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Answer:

Correct Answer: 5. (c)

Solution:

  1. As we know that, a vector coplanar to a,b and orthogonal to c is λ(a×b)×c.

A vector coplanar to (2i^+j^+k^),(i^j^+k^) and orthogonal to 3i^+2j^+6k^

=λ[(2i^+j^+k^)×(i^j^+k^)×(3i^+2j^+6k^)]=λ[(2i^j^3k^)×(3i^+2j^+6k^)]=λ(21j^7k^)

Unit vector =+(21j^7k^)(21)2+(7)2=+(3j^k^)10



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