## Vector Dot Product

What is the dot product of [V•W]?

Hint
The dot product, or scalar product, is an mathematical operation that takes two vectors and returns a single number. It is the projection of vector B onto vector A multiplied by the determinant of vector A.
Hint 2
The dot product of vectors A and B:
$$A\cdot B=a_xb_x+a_yb_y+a_zb_z=|A||B|cos\theta =B\cdot A$$$where $$A=a_x\textbf{i}+a_y\textbf{j}+a_z\textbf{k}$$ , $$B=b_x\textbf{i}+b_y\textbf{j}+b_z\textbf{k}$$ , $$|A|$$ is the determinant of vector A, and $$|B|$$ is the determinant of vector B. The dot product, or scalar product, is an mathematical operation that takes two vectors and returns a single number. It is the projection of vector B onto vector A multiplied by the determinant of vector A. The dot product of vectors A and B: $$A\cdot B=a_xb_x+a_yb_y+a_zb_z=|A||B|cos\theta =B\cdot A$$$
where $$|A|$$ is the determinant of vector A, $$|B|$$ is the determinant of vector B, and:
$$A=a_x\textbf{i}+a_y\textbf{j}+a_z\textbf{k}$$
$$B=b_x\textbf{i}+b_y\textbf{j}+b_z\textbf{k}$$
Remember, vector W can be written as $$W=1i-2j+3k$$ . Thus,
$$V\cdot W=v_xw_x+v_yw_y+v_zw_z$$$$$=(6)(1)+(2)(-2)+(-7)(3)=6-4-21=-19$$$
-19