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

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To find the angle between the vectors v = -5√3i + 5j and w = 5i using the dot product formula, the equation cos(θ) = (v · w) / (|v| |w|) is applied. The dot product of the vectors is calculated as v · w = (-5√3)(5) + (5)(0) = -25√3. The magnitudes of the vectors are |v| = √((-5√3)² + 5²) and |w| = 5. By substituting these values into the formula, the angle θ can be determined.
brinlin
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Find the angle between the vectors $$v=-5\sqrt{3}i+5j$$ and $$w=5i$$
 
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I'd use the dot product formula ...

$\cos{\theta} = \dfrac{\vec{v} \cdot \vec{w}}{|v| \, |w|}$
 
when we use the dot product formula. What would we plug in for v and w.
 
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
 
brinlin said:
when we use the dot product formula. What would we plug in for v and w.
? YOU said, in your first post that
$v= -5\sqrt{3}i+ 5j$
$w= 5i$.
 

Thread 'Area of Overlapping Squares'

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