Find the value of λ so that the vectors 2i^−4j^+k^ and 4i^−8j^+λk^ are perpendicular.Review Later-1510-4020
Question
Find the value of λ so that the vectors 2i^−4j^+k^ and 4i^−8j^+λk^ are perpendicular.Review Later-1510-4020
Solution
The vectors A = 2i - 4j + k and B = 4i - 8j + λk are perpendicular if their dot product is zero.
The dot product of two vectors A = a1i + a2j + a3k and B = b1i + b2j + b3k is given by:
A.B = a1b1 + a2b2 + a3*b3
So, for the given vectors, we have:
A.B = (24) + (-4-8) + (1*λ) = 0
This simplifies to:
8 + 32 + λ = 0
Solving for λ gives:
λ = -40
So, the value of λ that makes the vectors perpendicular is -40.
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