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प्रश्न
If `veca = 2hati + hatj + 2hatk` and `vecb = 5hati - 3hatj + hatk`, find the projection of `vecb` on `veca`.
उत्तर
Given, `veca = 2hati + hatj + 2hatk`
And `vecb = 5hati - 3hatj + hatk`
Projection of `vecb` on `veca = 1/|veca|(veca . vecb)`
`(veca . vecb)` = (2 × 5) + (1 × (– 3)) + (2 × 1)
= 10 – 3 + 2
= 9
Magnitude of `|veca| = sqrt(2^2 + 1 + 2^2)`
= `sqrt(4 + 1 + 4)`
= `sqrt(9)`
= 3
∴ Required projection = `9/3` = 3
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