#vecu=4hati+7hatj+5hatk# and #vecv=5hati+3hatj+4hatk#; #u*v=#?

2 Answers
Dec 24, 2017

#vec(u) * vec(v) = 61#

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

#vecu*vecv = 61#

Explanation:

Use the definition:

#u*v = (u_(hati))(v_(hati))+(u_(hatj))(v_(hatj))+ (u_(hatk))(v_(hatk))#

#vecu*vecv = (4)(5)+(7)(3)+ (5)(4)#

#vecu*vecv = 61#