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प्रश्न
If the vectors `2hati-qhatj+3hatk and 4hati-5hatj+6hatk` are collinear, then value of q is
(A) 5
(B) 10
(C) 5/2
(D) 5/4
उत्तर
(C) 5/2
Let `bar a=2hati-qhatj+3hatk and barb=4hati-5hatj+6hatk`
Since, `bara and barb` are collinear.
∴ there exists a scalar t such that `barb = t bara `.
∴ `4hati-5hatj+6hatk=t(2hati-qhatj+3hatk)=2thati-qthatj+3thatk`
∴ By equality of vectors, we get
4 = 2t, - 5 = - qt, 6 = 3t
∵ 4 = 2t and 6 = 3t ∴t = 2
- 5 =- q(2)
–5 = – 2q
∴ 5 = 2q
q = 5/2
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