Find a vector whose length is 7 and that is perpendicular to each of the vectors
`vec(A) = 2 hat(i) - 3 hat(j) + 6 hat(k) and vec(B) = hat(i) + hat(j) - hat(k)`

Explanation

Given : `vec(A) = 2 hat(i) - 3 hat(j) + 6 hat(k)`
`vec(B) = hat(i) + hat(j) - hat(k)`
Here ` vec(A) xx vec(B) |{:(hat(i),hat(j), hat(j)),(2, -3, 6),(1 , 1, -1):}|`
`= hat(i) (3 - 6) - hat(j) (-2 - 6) + hat(k) (2 + 3)`
`= - 3 hat(i) + 8 hat(j) + 5 hat(k)`
`|A^(2) xx vec(B)| = sqrt((-3)^(2) + 8 ^(2) + 5^(2))`
`= sqrt(98) = 7 sqrt(2)`
Unit vector perpendicular to `vec(A) and vec(B)` is
`hat(n) = (vec(A) xx vec(B))/(|vec(A) xx vec(B)|)= (-3 hat(i) + 8 hat(j) + 5 hat(k))/(7 sqrt(2))`
Required vector
`= 7 hat(n) = 7 ((-3hat(i) + 8 hat(j) + 5 hat(k))/(7 sqrt(2)))`
`= (1)/(sqrt(2)) ( - 3 hat(i) + 8 hat(j) + 5 hat(k))`