How do you compute the dot product for u=4i-2ju=4i2j and v=i-jv=ij?

1 Answer
Sep 30, 2016

u•v = 6uv=6

Explanation:

For any two vectors ,u and v, of the form:

(u_i)hati + (u_j)hatj(ui)ˆi+(uj)ˆj

and

(v_i)hati + (v_j)hatj(vi)ˆi+(vj)ˆj

The dot product is:

u•v = (u_i)(v_i) + (u_j)(v_j)uv=(ui)(vi)+(uj)(vj)

Substituting the given values:

u•v = (4)(1) + (-2)(-1)uv=(4)(1)+(2)(1)

u•v = 6uv=6

Note: For 3 dimensions the dot product extends to:

u•v = (u_i)(v_i) + (u_j)(v_j) + (u_k)(v_k)uv=(ui)(vi)+(uj)(vj)+(uk)(vk)