Question

What is the dot product of `(2i -3j + 4k)` and `(i + j -7k)`?

Answer 1

`v_1*v_2=-29`

Explanation:

I'm going to name these two vectors as `v_1` and `v_2`, where `v_1=2i-3j+4k=<2,-3,4>` and `v_2=i+j-7k=<1,1-7>`.

The dot product of two vectors is defined as `v_1*v_2=||v_1|| ||v_2|| cos(theta)=(i_1)(i_2)+(j_1)(j_2)+(k_1)(k_2)`.

We don't have an angle to use, so we'll calculate the dot product using by adding the products of the components.

Therefore, `v_1*v_2=(2)(1)+(-3)(1)+(4)(-7)=2-3-28=-29`.

Answer 2

The dot product is `=-29`

Explanation:

The dot product of `2` vectors

`veca= < x_1, y_1,z_1>`

and

`vecb= < x_2, y_2,z_2 >`

is

`veca.vecb = < x_1, y_1,z_1> . < x_2, y_2,z_2 >`

`=x_1x_2 +y_1y_2+z_1z_2`

Here, we have

`<2, -3, 4> . <1, 1, -7 = (2)*(1)+(-3)*(1)+(4)*(-7)`

`=2-3-28`

`=-29`