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Q.

What is the condition for the vectors 2i^+3j^-4k and 3i^-aj^+bk^ to be parallel ?

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a

a = 4, b = 5

b

a = 8, b = 2

c

a = –6, b = –9/2 

d

a = –9/2, b = – 6

answer is A.

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Detailed Solution

If the cross product of two vectors is zero, then the two vectors must be parallel. i.e

A×B=0

(2i^+3j^-4k^)×(3i^-aj^+bk^)=0

(3b-4a)i^+-12-2bj^+(-2a-9)k^=0

Given that the vector on the right hand is 0

122b=04  and 2a9=0

b=6 and a=-92

Hence the correct answer is a=-92,b=-6.

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