1. ## Interpreting Scalar Product (formula in equations), Please help!

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 = xy (1)

and
xy = |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 = b
1i + 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.

ab = (a1b1) + (a2b2) (5)

|a| = √ ̅ (a12+ a22) (6)

|b| =
√ ̅ (b12+ b22 ) (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).

2. ## Re: Interpreting Scalar Product (formula in equations), Please help!

What have you been able to do so far? Knowing that will enable us to help you better.

-Dan

3. ## Re: Interpreting Scalar Product (formula in equations), Please help!

Hi Dan, unfortunately I have not attempted it as of yet as I am unsure on how to answer these particular questions, I would appreciate any help if possible, thank you! 4. ## Re: Interpreting Scalar Product (formula in equations), Please help!

One way to do the dot product of two vectors is defined as: $\displaystyle x = a i + b j$, $\displaystyle y = c i + d j$, $\displaystyle x \cdot y = (a c) + (b d)$ (Line 5)

a) So what is the dot product of $\displaystyle x = 3 i - 6 j$ and $\displaystyle y = 8 i - 2 j$? (From lines 8 and 9.)

b) Now that you have $\displaystyle x \cdot y$ can you use equation 2 to find $\displaystyle \theta$?

-Dan

5. ## Re: Interpreting Scalar Product (formula in equations), Please help!

Thank you for the help Dan.