Question

For each pair of vectors u and v with angle θ between them, sketch the resultant.|u| = 12, |v| = 20, θ = 27°

Accepted Answer

Identify the given information: the magnitudes of vectors $$ \mathbf{u} $$ and $$ \mathbf{v} $$ are $$ |\mathbf{u}| = 12 $$ and $$ |\mathbf{v}| = 20 $$, and the angle between them is $$ 	heta = 27^\circ . $$Recall that the resultant vector $$ \mathbf{R} = \mathbf{u} + \mathbf{v} $$ can be found using the Law of Cosines for vectors, where the magnitude of $$ \mathbf{R}  is $$given by:

$$ 
|\mathbf{R}| = \sqrt{|\mathbf{u}|^2 + |\mathbf{v}|^2 + 2 |\mathbf{u}| |\mathbf{v}| \cos(	heta)} 
 To $$sketch the resultant, start by drawing vector $$ \mathbf{u} $$ with length proportional to 12 units in any direction you choose. Next, from the tip of $$ \mathbf{u} $$, draw vector $$ \mathbf{v}  at an $$angle of $$ 27^\circ $$ relative to $$ \mathbf{u} $$, with length proportional to 20 units. The resultant vector $$ \mathbf{R}  is $$then drawn from the tail of $$ \mathbf{u}  ($$the starting point) to the tip of $$ \mathbf{v}  ($$the ending point). This vector represents the sum $$ \mathbf{u} + \mathbf{v} .$$

For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 12, |v| = 20, θ = 27°

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Key Concepts

Vector Addition

Law of Cosines for Vectors

Angle Between Vectors