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+1 vote
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in Vector algebra by (52.5k points)

Let  vector u be a vector coplanar with the vectors a = 2i + 3j - k and b = j + k. If vector u  is perpendicular to a and u.b = 24, then |u|2  is equal to 

(A) 315 

(B) 256 

(C) 84 

(D) 336

1 Answer

+1 vote
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Best answer

Answer is (D) 336

Since all three given vectors are coplanar, we get

Adding Eqs. (2) and (3), we have

2x + 2z = 24

x + z = 12 (4)

Now, substituting the value of y from Eq. (2) and value of x from Eq. (4) in Eq. (1), we get

24 – 2z + 3 (24 – z) – z = 0

That is, 96 = 6z

⇒ z = 16

and hence x = −4 and y = 8.

Therefore,

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