## Vector Dot Product

What is the dot product of [V•W]?

##
__
__**Hint**

**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.

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__**Hint 2**

**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