1.

If a=(2, 1, -1), b=(1, -1, 0), c=(5, -1, 1), then unit vector parallel to a + b - c but in opposite direction is

Answer»

`(1)/(3)(2hati-hatj+2hatk)`
`(1)/(2)(2hati-hatj+2hatk)`
`(1)/(3)(2hati-hatj-2hatk)`
None of these

Solution :Let a = (2, 1, -1), B = (1, -1, 0) and C = (5, -1, 1)
Then, `a+b-c=(2+1-5)hati+(1-1+1)hati+(-1+0-1)hatk`
`=-(2hati-hatj+2hatk)`
`because` Unit VECTOR of `(a+b-c)=-((2hati-hatj+2hatk))/(3)`
`therefore` Required unit vector of `(a+b-c)=((2hati-hatj+2hatk))/(3)`


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