#vecu=4hati+7hatj+5hatk# and #vecv=5hati+3hatj+4hatk#; #u*v=#?
2 Answers
Dec 24, 2017
Explanation:
The dot product of two vectors is the sum of the products of the corresponding coefficients of the unit base vectors.
That is:
#< u_1, u_2, u_3 > * < v_1, v_2, v_3 > = u_1 v_1 + u_2 v_2 + u_3 v_3#
So in our example:
#vec(u) * vec(v) = < 4, 7, 5 > * < 5, 3, 4 >#
#color(white)(vec(u) * vec(v)) = 4*5+7*3+5*4#
#color(white)(vec(u) * vec(v))= 20+21+20#
#color(white)(vec(u) * vec(v))= 61#
Dec 24, 2017
Explanation:
Use the definition: