Question

Find the dot product of the given vectors.
u= -5i + 3j
v=3i + 4i

Answer 1

`\mathbf{a}\cdot \mathbf{b}=-3`

Explanation:

The dot product of vectors.

Given two vectors a and b in their rectangular form:

`\mathbf{a}= a_x\mathbf{i}+a_y\mathbf{j}`

`\mathbf{b}= b_x\mathbf{i}+b_y\mathbf{j}`

The dot product of the vectors is a scalar with value:

`\mathbf{a}\cdot \mathbf{b}=a_x.a_y+b_x.b_y`

The given vectors are:

`\mathbf{u}= -5\mathbf{i}+3\mathbf{j}`

`\mathbf{v}= 3\mathbf{i}+4\mathbf{j}`

Calculating the dot product:

`\mathbf{a}\cdot \mathbf{b}=(-5)(3)+(3)(4)=-15+12=-3`

`\mathbf{a}\cdot \mathbf{b}=-3`