If a = i +2 j +3 k , b =- i +2 j + k , c = i +2 j -2 k , n is perpendicular to both a and b and is the angle between c and n then =

Step-by-step solution

We have, n a and n b aligned & n = a b & = | array ccc i & j & k 1 & 2 & 3 -1 & 2 & 1 array |=-4 i-4 j+4 k & Again, = | n c | | n || c | & Now, n c = | array ccc i & j & k -4 & -4 & 4 1 & 2 & -2 array | & =-4 j -4 k & = |-4 j -4 k | |-4 i -4 j +4 k || i +2 j -2 k | & = (-4)^2+(-4)^2 (-4)^2+(-4)^2+(4)^2 (1)^2+(2)^2+(-2)^2 & = 16+16 16+16+16 1+4+4 = 4 2 (4 3 ) 3 = 2 3 3 & aligned