If a vector 2 i +3 j +8 k is perpendicular to the vector 4 j -4 i + k , then the value of is

Step-by-step solution

Two vectors must be perpendicular if their dot product is zero. Let, aligned a & =2 i +3 j +8 k b & =4 j -4 i + k & =-4 i +4 j + k aligned According to the above hypothesis a b a b =0 array lc & (2 i +3 j +8 k ) (-4 i +4 j + k )=0 & -8+12+8 =0 & 8 =-4 & =- 4 8 =- 1 2 array NOTE: a b =a b . Here, a and b are always positive as they are the magnitudes a and b .