Question

given the following vectors, calculate $-2\mathbf{u}+3\mathbf{v}$.

$\mathbf{u}=\langle 1,2\
angle,\mathbf{v}=\langle 8,-10\
angle$

Explanation:

Step1: Multiply vectors by scalars

$$ -2\mathbf{u}=-2\langle1,2 angle=\langle-2\times1,-2\times2 angle=\langle - 2,-4 angle $$

$$ 3\mathbf{v}=3\langle8,-10 angle=\langle3\times8,3\times(-10) angle=\langle24,-30 angle $$

Step2: Add the resulting vectors

$$ -2\mathbf{u}+3\mathbf{v}=\langle - 2,-4 angle+\langle24,-30 angle=\langle-2 + 24,-4+( - 30) angle=\langle22,-34 angle $$

Answer:

$\langle22,-34
angle$