Mathematics

Problem

If the direction cosines of a vector satisfy

l=\tfrac{1}{3}

and

m=\tfrac{2}{3}

with

n>0

, find the value of

n

. a)

\dfrac{\sqrt{5}}{3}

\tfrac{2}{3}

\dfrac{1}{\sqrt{3}}

\dfrac{\sqrt{2}}{3}

Intuitive explanation

Direction cosines are the cosines of the angles a vector makes with the coordinate axes, and they're always constrained by a fundamental identity: $l^2 + m^2 + n^2 = 1$ . This constraint comes from the fact that these three angles must be geometrically consistent. You already know two of the three direction cosines, so you can substitute them into this identity and solve for the unknown $n$ —just remember to pick the positive root since you're told $n > 0$ .

Intuitive explanation

Browse the problem library