MHB What is the Angle Between Vectors Using the Dot Product Formula?

[brinlin]

Find the angle between the vectors $$v=-5\sqrt{3}i+5j$$ and $$w=5i$$

 

[skeeter]

I'd use the dot product formula ...

$\cos{\theta} = \dfrac{\vec{v} \cdot \vec{w}}{|v| \, |w|}$

 

[brinlin]

when we use the dot product formula. What would we plug in for v and w.

 

[skeeter]

to calculate the dot product of two vectors given in component form …

$(a \vec{i} + b \vec{j}) \cdot (c \vec{i} + d \vec{j}) = ac + bd$

… note the dot product is a scalar quantity

 

[HOI]

when we use the dot product formula. What would we plug in for v and w.

? YOU said, in your first post that
$v= -5\sqrt{3}i+ 5j$
$w= 5i$.