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Vector Algebra

Question
CBSEENMA12035939
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For what value of ‘a’ the vectors   2 i^  - 3 j^ + 4 k    and   a i^  + 6 j^  - 8 k   are collinear?

Solution

Two vectors  x→  and  y→  are collinear if  x→ = λ y→,   where  λ  is a constant.Now, the vectors  2 i^ - 3 j^ + 4 k   and     a i^ + 6 j^ - 8 k    are collinear,∴  2 i^ - 3 j^ + 4 k   = λ  a i^ + 6 j^ - 8 k ,  where  λ  is a constant.⇒ 2 = λ a,    - 3 = 6 λ,     4 = - 8 λ⇒ Now,  - 3 = 6 λ      or      4 = -  8 λ   ⇒   λ  = - 122 = λ a⇒ 2 = - 12 x a⇒ a = - 4

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