The vector perpendicular to the vectors 4 i - j +3 k and -2 i + j -2 k whose magnitude is 9

Step-by-step solution

Let a =4 i - j +3 k , b =-2 i + j -2 k and c =x i +y j +z k Given, a c =0 i.e., 4 x-y+3 z=0 ...(i) and b. c =0 i.e., -2 x+y-2 z=0 ...(ii) Also, | c |=9 i.e., x²+y²+z²=81 ...(iii) Now, from Eqs. (i) and (ii), we get 2 x+z=0 z=-2 x On putting this value in Eq. (iii), we get aligned x²+y²+4 x² &=81 5 x²+y² &=81...(iv) aligned On multiplying Eq. (i) by 2 and Eq. (ii) by 3 and then adding, we get array r 8 x-2 y+6 z=0 -6 x+3 y-6 z=0 2 x+y=0 y=-2 x array On putting this value in Eq. (iv), we get 5 x²+4 x²=81 array lcc &