1.

A unit vector perpendicular to each of the vectors 2hat(i)-hat(j)+hat(k)and 3hat(i)-4hat(j)-hat(k) is

Answer»

`(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(J)-(1)/(sqrt(3))hat(K)`
`(1)/(sqrt(2))hat(i)+(1)/(2)hat(j)+(1)/(2)hat(k)`
`(1)/(sqrt(3))hat(i)-(1)/(sqrt(3))hat(j)-(1)/(sqrt(3))hat(k)`
`(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)+(1)/(sqrt(3))hat(k)`

SOLUTION :`|(hat(i),hat(j),hat(k)),(2,-1,1),(3,-4,-1)|`
`=hat(i)(1+4)-hat(j)(-2-3)+hat(k)(-8+3)`
`=5hat(i)+5hat(j)-5hat(k)`
Unit vector `=(5)/(5sqrt(3))hat(i)+(5)/(5sqrt(3))hat(j)-(5)/(5sqrt(3))hat(k)`
`=(1)/(sqrt(3))hat(i)+(1)/(sqrt(3))hat(j)-(1)/(3sqrt(3))hat(k)`


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