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प्रश्न
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors `veca = 2i + 3hatj - hatk` and `vecb = hati - 2hatj + hatk`.
उत्तर
We have `veca = 2hati + 3hatj - hatk, vecb = hati - 2hatj + hatk`
Let be the resultant of c and a.
Then,
`vecc = veca + vecb = (2 + 1)hati + (3 - 2)hatj + (-1 + 1)hatk = 3hati + hatj`
`|vecc| = sqrt(3^2 + 1^2) = sqrt(9 + 1) = sqrt10`
`hatc = vecc/|vecc| = (3hati + hatj)/sqrt10`
Therefore, the resultant is a vector of five units that is parallel to the results of vectors a and b.
⇒ `±5.c = ±5 xx (1/sqrt10)(3hati + hatj) `
`= ±(3sqrt10hati)/2 ± sqrt10/2hatj`.
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`veca = 4hati - hatj + hatk` and `vecb = -2hati + hatj - 2hatk`
