If u is a unit vector, find u · v and u · w. (assume v and w are also unit vectors.) equilateral triangle

solution:

we know that,

u. v = ΙuΙ ΙvΙcosθ

here,

θ = 60° (since the given triangle is equilateral triangle)

u. v = ΙuΙ ΙvΙcos60°

= 1 x 1 x 1/2

u. v = 1/2

now, u. w = ΙuΙ ΙwΙcosθ

= ΙuΙ x cos (60x2)

u. w = - 1/2