Vectors 1 Question 18

19. Let a=2i^j^+k^,b=i^+2j^k^ and c=i^+j^2k^ be three vectors. A vector in the plane of b and c, whose projection on a is of magnitude 2/3, is

(1993, 2M)

(a) 2i^+3j^3k^

(b) 2i^+3j^+3k^

(c) 2i^j^+5k^

(d) 2i^+j^+5k^

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Answer:

Correct Answer: 19. (3)

Solution:

  1. Given vectors are a=2i^j^+k^,b=i^+2j^k^ and c=i^+j^2k^. Any vector r in the plane of b and c is r=b+t(c)=i^+2j^k^+t(i^+j^2k^)

=(1+t)i^+(2+t)j^(1+2t)k^

Since, projection of r on a is 23.

ra|a|=23

|2(1+t)(2+t)(1+2t)6|=23|(1+t)|=2t=1 or 3

On putting t=1,3 in Eq. (i) respectively, we get

r=2i^+3j^3k^ or r=2i^j^+5k^



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