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प्रश्न
A unit vector `hata` makes equal but acute angles on the coordinate axes. The projection of the vector `hata` on the vector `vecb = 5hati + 7hatj - hatk` is ______.
विकल्प
`11/15`
`11/(5sqrt(3))`
`4/5`
`3/(5sqrt(3))`
उत्तर
A unit vector `hata` makes equal but acute angles on the coordinate axes. The projection of the vector `hata` on the vector `vecb = 5hati + 7hatj - hatk` is `underlinebb(11/15)`.
Explanation:
Let θ be the equal acute angle with coordinate axes.
`\implies` l = m = n = cos θ and l2 + m2 + n2 = 1
`\implies` 3l2 = 1
`\implies` l = `1/sqrt(3)`
So `veca = (1/sqrt(3) hati + 1/sqrt(3) hatj + 1/sqrt(3) hatk)`
and projection on b = `5hati + 7hatj - hatk` is given by
`(veca. vecb)/|b| = ((5 + 7 - 1)/sqrt(3))/sqrt(25 + 49 + 1)`
= `11/sqrt(225)`
= `11/15`.
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