The diagonals of a parallelogram are the vectors 3 i +6 j -2 k . and - i -2 j -8 k . Then the length of the shorter side of parallelogram is

Step-by-step solution

Let a and b be the length of the sides of the parallelogram and d ₁, d ₂ be the length of diagonals. Given, aligned d ₁ &=3 i +6 j -2 k d ₂ &=- i -2 j -8 k aligned a = d ₁+ d ₂ 2 = 2 i +4 j -10 k 2 = i +2 j -5 k | a |= 1+4+25 = 30 and b = d ₁- d ₂ 2 = 4 i +8 j +6 k 2 =2 i +4 j +3 k | b |= 4+16+9 = 29