How do you compute the dot product for #u=4i-2j# and #v=i-j#?

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Answer 1 · 2016-09-30T01:40:32

#u•v = 6#

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

#(u_i)hati + (u_j)hatj#

and

#(v_i)hati + (v_j)hatj#

#u•v = (u_i)(v_i) + (u_j)(v_j)#

Substituting the given values:

#u•v = (4)(1) + (-2)(-1)#

#u•v = 6#

Note: For 3 dimensions the dot product extends to:

#u•v = (u_i)(v_i) + (u_j)(v_j) + (u_k)(v_k)#