If `veca = (hati + hatj + hatk), vecb = (4hati - 2hati + 3hatk)` and `vecc = (hati - 2hatj + hatk)`, find a vector of magnitude 6 units which is parallel to the vector `(2veca - vecb + 3vecc)`.

If `veca = (hati + hatj + hatk), vecb = (4hati - 2hati + 3hatk)` and `

1.	If `veca = (hati + hatj + hatk), vecb = (4hati - 2hati + 3hatk)` and `vecc = (hati - 2hatj + hatk)`, find a vector of magnitude 6 units which is parallel to the vector `(2veca - vecb + 3vecc)`.
Answer» We have, `(2veca - vecb + 3vecc) = 2(hati + hatj + hatk) - (4hati - 2hatj + 3hatk) + 3(hati-2hatj +hatk)` `= (2-4+3) hati + (2+2-6)hatj + (2-3+3) hatk` `= (2hati - 2hatj + 2hatk)`. Unit vectors parallel to `(2veca - vecb + 3vecc)` are `+- ((hati - 2hatj + 2hatk))/(sqrt(1^(2) + (-2)^(2) + 2^(2))) = +- 1/3(hati - 2hatj + 2hatk)` . Required vectors of magnitude of 6 units are `+-{6xx 1/3(hati - 2 hatj+ 2hatk)} = +- 2(hati - 2hatj + 2hatk)`.

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