Question

If u = 4, 3, 8 and if v= 7, 2, -3,what is the dot product?

Answer 1

The dot product of two vectors

`a=a_1i+a_2j+a_3kandb=b_1i+b_2j+b_3k`

Is given as

`\begin{gathered} a\mathrm{}b=a_1b_1+a_2b_2+a_3b_3 \\ where,_{} \\ a_1=4,a_2=3,a_3=8_{} \\ b_1=7,b_2=2,b_3=-3 \end{gathered}`

By substitution, we will have that

`\begin{gathered} a.b=(4*7)+(3*2)+(8*-3) \\ a.b=28+6-24 \\ a.b=10 \end{gathered}`

Hence,

The dot product of u(4,3,8) and v(7,2,-3) is = 10