Find a unit vector that is orthogonal to both ( i+j ) and ( i+k ) .?

Answer 1

Suppose the unknown vector is ai + bj + ck. The orthogonal conditions say that the dot products with i + j and i + k are both 0. Thus, a + b = 0 and a + c = 0; that is, b = -a and c = -a, so the unknown vector is ai - aj - ak. But the length of this is sqrt(a^2 + a^2 + a^2) = asqrt(3), which is a unit vector if and only if a = 1/sqrt(3)

Therefore, the unknown vector is (1/sqrt(3))i - (1/sqrt(3))j - (1/sqrt(3)k.

Answer 2

orthogonal
does that mean _|_ ??
if so

i - j
&

( i+k )= i+kj or what ??