Dot product of two perpendicular vectors will be zero. Therefore,
(ai^+bj^+k^)⋅(2i^−3j^+4k^)=0
⇒2a−3b+4=0...Eq(1)
As given in the question,
3a+2b=7...Eq(2)
From both equations, we get a=1&b=2
Then,
ba=2x⇒x=b2a=22×1
⇒x=1
JEE Main 2023 — Physics Mechanics
Vectors ai^+bj^+k^ and 2i^−3j^+4k^ are perpendicular to each other when 3a+2b=7, the ratio of a to b is 2x. The value of x is _____.
Held on 24 Jan 2023 · Verified 6 Jul 2026.
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