Use the dot product to find the value of the scalar, given that...

Question

Use the dot product to find the value of the scalar, given that 𝑣⃗ =4𝑖⃗+𝑗⃗ and 𝑤⃗ =3𝑖⃗−8𝑗⃗.

2(𝑣⃗∙𝑤⃗)

Hello! I need help with solving this whole problem, please :)

Answer 1

The dot product is defined as follows:

v • w = ||v|| ||w|| cos(θ) = (i₁)(i₂) + (j₁)(j₂) where i₁, i₂, j₁, j₂ are defined above. Therefore,

v • w = (4)(3) + (1)(-8) = 12 - 8 = 4

Therefore 2(v • w) = 2(4) = 8