For the given vectors [tex] \vec{a}=a_{1}\hat{i}+a_{2}\hat{j} [/tex] and [tex] \vec{b}=b_{1}\hat{i}+b_{2}\hat{j} [/tex]
The dot product of vectors a and b is defined as = [tex] \vec{a}.\vec{b}=(a_{1}\times b_{1}+a_{2} \times b_{2}) [/tex]
So, [tex] \vec{a}.\vec{b} = (4\hat{i}+3\hat{j}). (-4\hat{i}+4\hat{j}) [/tex]
[tex] \vec{a}.\vec{b}=(4\times(-4)+3 \times4) [/tex]
= -16+12
= -4
