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Question
Projection vector of `vec"a"` on `vec"b"` is ______.
Options
`((vec"a"*vec"b")/|vec"b"|^2)vec"b"`
`(vec"a"*vec"b")/|vec"b"|`
`(vec"a"*vec"b")/|vec"a"|`
`((vec"a"*vec"b")/|vec"a"|^2)vec"b"`
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Solution
Projection vector of `vec"a"` on `vec"b"` is `((vec"a"*vec"b")/|vec"b"|^2)vec"b"`.
Explanation:
Let `vec"a"` and `vec"b"` be two vectors represented by `vec"OA"` and `vec"OB"` respectively.
Now `vec"a"*vec"b" = |vec"a"||vec"b"| cos theta`
= `|vec"b"|(|vec"a"|costheta)`
= `|vec"b"|("OA" cos theta)`
= `|vec"b"|("OL")`
⇒ OL = `(vec"a" * vec"b")/|vec"b"|`
⇒ Projection of vector `vec"a"` on `vec"b" = (vec"a"*vec"b" vec"b")/(|vec"b"| |vec"b"|)`
= `(vec"a"*vec"b")/|vec"b"|^2 vec"b"`
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