Finding the Angle Between Two Vectors Using the Dot Product

The dot product formula is a useful tool for determining the angle between two vectors. According to this formula, the dot product of two vectors is equivalent to the multiplication of their magnitudes and the cosine of the angle that separates them. With some manipulation of this formula, we are able to isolate and solve for the angle between the vectors.

The problems about Finding the Angle Between Two Vectors Using the Dot Product

Topic	Problem	Solution
None	Given $v = - 7 i - 6 j$ and…	Given vectors $v = - 7 i - 6 j$ and $w = 5 i - j$ ,…
None	Find the angle, $α$ , between the vectors…	\(\cos\alpha = \frac{\overrightarrow{u} \cdot \overrightarrow{w}}{\|\|\overrightarrow{u}\|\| \|\|\overrig…
None	Find the angle between $2 \mathbf{i}+5 \mathbf{j}…	Given vectors $A = 2 i + 5 j$ and $B = j$ .
None	Find the angle $θ$ (in degrees) between the …	We are given the vectors $u = 3 i - 6 j$ and \(\mathbf{v} = 9\mathbf{i} …
None	Given the vectors $\vec{u} = 7 i + 10 j$ and $\vec{v}…	Given the vectors $\vec{u} = 7 i + 10 j$ and $\vec{v} = 3 i + 2 j$ , we are to find the angle (in degree…