Dot Prod
What is the dot product of [Vâ˘W]?
Expand 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
$$W=0i+1j$$
. Thus,
$$$V\cdot W=v_xw_x+v_yw_y=(2)(0)+(7)(1)=0+7=7$$$
7
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