Hello all,

I have recently been advancing my knowledge of mathematics by working through worksheets online. However, I am stumped at these particular questions, and have no clue where to begin and answer! Any chance of any explanations and answers? All responses are highly appreciated, Thank you everyone! P.S I have added a file attachment of the questions below which is little clearer than what I have typed out

The dot scalar product (M) of two directional paths 'x' and 'y' is mathematically defined as follows:

M = x∙y (1)

and

x∙y = |x||y|cos0 (2)

where |x| is the magnitude of directional path 'x' and |y| is the magnitude of directional path 'y' and 0 is the angle between paths 'x' and 'y'

Generally, for two directional paths 'a' and 'b' defined as follows:

a = a1i + a2j (3)

b = b1i + b2j (4)

The following formulas are given for the dot or scalar product of ‘a’ and ‘b’ and their respective magnitudes. Remember the notations ‘i’ and ‘j’ represent the spatial direction of the paths.

a∙b = (a1b1) + (a2b2) (5)

|a| = √ ̅ (a1^{2}+ a2^{2}) (6)

|b| = √ ̅ (b1^{2}+ b2^{2 }) (7)

If the directional paths ‘x’ and ‘y’ are defined as follows:

x = 3i + 6j (8)

y = 8i - 2j (9)

Question a.

Solve for M by interpreting all the given formulas in equations (1) to (9).

Question b.Solve for the angle between the directional paths ‘x’ and ‘y’ by making the subject of the formula in equation (2).