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Question
Find the value of λ such that the vectors `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"` are orthogonal ______.
Options
0
1
`3/2`
`- 5/2`
Solution
Find the value of λ such that the vectors `vec"a" = 2hat"i" + lambdahat"j" + hat"k"` and `vec"b" = hat"i" + 2hat"j" + 3hat"k"` are orthogonal `- 5/2`.
Explanation:
Given that `vec"a" = 2hat"i" + lambdahat"j" + hat"k"`
And `vec"b" = hat"i" + 2hat"j" + 3hat"k"`
Since `vec"a"` and `vec"b"` are orthogonal
∴ `vec"a" * vec"b"` = 0
⇒ `(2hat"i" + lambdahat"j" + hat"k") * (hat"i" + 2hat"j" + 3hat"k")` = 0
⇒ 2 + 2λ + 3 = 0
⇒ 5 + 2λ = 0
⇒ λ = `(-5)/2`
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