Question

(2 points) Determine the scalar product of A= 6.0i + 4.0j - 2.0k andB = 5.0i - 6.0 j- 3.0 k.

Answer 1

The scalar product or dot product of any two vectors is the product of magnitudes of the two vectors and the cosine of the angle between them.

If $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ are the two vectors include with an angle $\theta$ ,then the scalar product of the two vectors is ,

$\underset{A}{\rightarrow}.\underset{B}{\rightarrow}$ = AB COS $\theta$

Scalar product can be written in terms of magnitude of their components as,

$\underset{A}{\rightarrow}$ = 6 i + 4 j - 2k

$\underset{B}{\rightarrow}$ = 5i -6j -3k

$\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ = ( 6* 5)( i.i) +( 4* -6)(j.j) +(-2 * -3)(k.k)

= 30 - 24 + 6

= 12 units

since i.i = j.j = k.k =1