Answer:
[tex]\mathbf{a}\cdot \mathbf{b}=-3[/tex]
Step-by-step explanation:
The dot product of vectors.
Given two vectors a and b in their rectangular form:
[tex]\mathbf{a}= a_x\mathbf{i}+a_y\mathbf{j}[/tex]
[tex]\mathbf{b}= b_x\mathbf{i}+b_y\mathbf{j}[/tex]
The dot product of the vectors is a scalar with value:
[tex]\mathbf{a}\cdot \mathbf{b}=a_x.a_y+b_x.b_y[/tex]
The given vectors are:
[tex]\mathbf{u}= -5\mathbf{i}+3\mathbf{j}[/tex]
[tex]\mathbf{v}= 3\mathbf{i}+4\mathbf{j}[/tex]
Calculating the dot product:
[tex]\mathbf{a}\cdot \mathbf{b}=(-5)(3)+(3)(4)=-15+12=-3[/tex]
[tex]\mathbf{a}\cdot \mathbf{b}=-3[/tex]
