If F =2 i + j - k and r =3 i +2 j -2 k , then the scalar and vector products of F and r have the magnitudes respectively as:

Step-by-step solution

aligned & F =2 i + j - k & r =3 i +2 j -2 k (given) aligned The scalar product of F and r is aligned F . r & =(2)(3)+(1)(2)+(-1)(-2) & =6+2+2=10 aligned The vector product of F and r is aligned F r & = | array ccc i & j & k 2 & 1 & -1 3 & 2 & -2 array | & = i [(1 -2)-(2 -1)]- j [(2 -2) & -(-1 3)]+ k [(2 2)-(3 1)] & = i (0)- j (-1)+ k (1)= j + k aligned Magnitude = (1)^2+(1)^2 = 2