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Show that the vectors 2i^-3j^+4k^ and -4i^+6j^- 8k^ are collinear. - Mathematics

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Question

Show that the vectors `2hati - 3hatj + 4hatk` and `-4hati + 6hatj -  8hatk` are collinear.

Sum

Solution

Let `veca = 2hati - 3hatj + 4hatk` and `vecb = -4hati + 6hatj - 8hatk`

It is observed that `vec b = -4hati + 6hatj - 8hatk `

`= -2(2hati - 3hatj + 4hatk) `

`= -2veca`

`therefore vec b = lambda vec a`

where,

λ = -2

Hence, the given vectors are collinear.

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Chapter 10: Vector Algebra - Exercise 10.2 [Page 440]

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NCERT Mathematics [English] Class 12
Chapter 10 Vector Algebra
Exercise 10.2 | Q 11. | Page 440

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