Answer to Question #86520 in Mechanics | Relativity for Joshua

Question

8.___ in analytic geometry of vector are the cosines of angles between the vector and the three coordinate axes
a.Direction sines
b.Direction Cosines
c.Direction tangents
d.All the options

9.if a=a1i+a2j+a3k and b=b1i+b2j+b3k
find a.b
a.a1b1−a2b2−a3b3
b.a1b1+a2b2−a3b3
c.a1b1−a2b2+a3b3
d.a1b1+a2b2+a3b3

Answer 1

8. b.

Direction Cosines

Source and more info:

https://en.wikipedia.org/wiki/Direction_cosine

9. d.

Considering that for unit vectors

$$i.i = j.j = k.k = 1; \\ i.j = j.k = i.k = 0; \\$$

The product will be

$$a.b = a_1b_1+a_2b_2+a_3b_3. \\$$

Here the dot (.) denotes scalar product.