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Question
Find λ, when the projection of `vec"a" = lambdahat"i" + hat"j" + 4hat"k"` on `vec"b" = 2hat"i" + 6hat"j" + 3hat"k"` is 4 units
Solution
The given vectors are `vec"a" = lambdahat"i" + hat"j" + 4hat"k"`, `vec"b" = 2hat"i" + 6hat"j" + 3hat"k"`
Also given that projection of a⃗ and b⃗ is 4 units.
`(vec"a" * vec"b")/|vec"b"|` = 4
`((lambdahat"i" + hat"j" + 4hat"k")*(2hat"i" + 6hat"j" + 3hat"k"))/|2hat"i" + 6hat"j" + 3hat"k"|` = 4
`((lambda)(2) + (1)(6) + (4)(3))/sqrt(2^2 + 6^2 + 3^2)` = 4
`(2lambda + 6 + 12)/sqrt(4 + 36 + 9)` = 4
`(2lambda + 18)/sqrt(49)` = 4
2λ + 18 = 4 × 7
2λ = 28 – 18
2λ = 10
⇒ λ = 5
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