Question

given vectors \\( \mathbf{a} = \langle 1, -5 \
angle \\) and \\( \mathbf{b} = \langle 2, 4 \
angle \\), find \\( 3\mathbf{a} + 4\mathbf{b} \\).
write your answer in component form.
\\( 3\mathbf{a} + 4\mathbf{b} = \langle \quad, \quad \
angle \\)

Explanation:

Step1: Calculate \(3\mathbf{a}\)

Given \(\mathbf{a}=\langle1,-5
angle\), then \(3\mathbf{a}=3\langle1,-5
angle=\langle3\times1,3\times(-5)
angle=\langle3,-15
angle\)

Step2: Calculate \(4\mathbf{b}\)

Given \(\mathbf{b}=\langle2,4
angle\), then \(4\mathbf{b}=4\langle2,4
angle=\langle4\times2,4\times4
angle=\langle8,16
angle\)

Step3: Calculate \(3\mathbf{a}+4\mathbf{b}\)

\(3\mathbf{a}+4\mathbf{b}=\langle3,-15
angle+\langle8,16
angle=\langle3 + 8,-15+16
angle=\langle11,1
angle\)

Answer:

\(\langle11,1
angle\)