Two adjacent sides of a parallelogram are 2 i -4 j +5 k and i -2 j -3 k , then the unit vector parallel to its diagonal is

Step-by-step solution

Let a and b be the adjacent sides of a parallelogram, where aligned & a =2 i -4 j +5 k & b = i -2 j -3 k aligned Let diagonal be c aligned c & = a + b c & =2 i -4 j +5 k + i -2 j -3 k & =3 i -6 j +2 k aligned Magnitude of aligned c & = 3^2+(-6)^2+(2)^2 & = 49 =7 aligned Unit vector in direction of diagonal c is aligned & = c | c | & = 1 7 (3 i -6 j +2 k ) & = 3 7 i - 6 7 j + 2 7 k aligned