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Multiplication with Vectors

If a⃗ =2î +...

Question

If $\to a = 2^i + l^j - 3^k$ and $\to b = 4^i - 3^j - 2^k$ are perpendicular to each other then find the value of scalar $λ$ ..

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Solution

Given: $\to a = 2^i + l^j - 3^k$ and $\to b = 4^i - 3^j - 2^k$ are perpendicular
$∴ \to a . \to b = 0$
$(2^i + λ^j - 3^k) (4^i - 3^j - 2^k) = 0$
$8 - 3 λ - 2 = 0$
$3 λ = 6$
$λ = \frac{6}{3} = 2$

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