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 answers? Answers would be appreciated as I can work through the steps logically to see how it works. All responses are highly appreciated, Thank you everyone! P.S I have added a file attachment of the questions below which is a 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 = xâˆ™y $\hspace{57px}$ (1)
and
xâˆ™y = xycosÎ¸ (2)
where x is the magnitude of directional path 'x' and y is the magnitude of directional path 'y' and Î¸ is the angle between paths 'x' and 'y'
Generally, for two directional paths 'a' and 'b' defined as follows:
a = a$_1$i + a$_2$j (3)
b = b$_1$i + b$_2$j (4)
The following formulas are given for the dot or scalar product of â€˜aâ€™ and â€˜bâ€™ and their respective magnitudes. Remember the notations â€˜iâ€™ and â€˜jâ€™ represent the spatial direction of the paths.
aâˆ™b = (a$_1$b$_1$) + (a$_2$b$_2$) (5)
a = âˆš(a$_1^2$ + a$_2^2$) (6)
b = âˆš(b$_1^2$ + b$_2^2$) (7)
If the directional paths â€˜xâ€™ and â€˜yâ€™ 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 â€˜xâ€™ and â€˜yâ€™ by making Î¸ the subject of the formula in equation (2).
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 answers? Answers would be appreciated as I can work through the steps logically to see how it works. All responses are highly appreciated, Thank you everyone! P.S I have added a file attachment of the questions below which is a 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 = xâˆ™y $\hspace{57px}$ (1)
and
xâˆ™y = xycosÎ¸ (2)
where x is the magnitude of directional path 'x' and y is the magnitude of directional path 'y' and Î¸ is the angle between paths 'x' and 'y'
Generally, for two directional paths 'a' and 'b' defined as follows:
a = a$_1$i + a$_2$j (3)
b = b$_1$i + b$_2$j (4)
The following formulas are given for the dot or scalar product of â€˜aâ€™ and â€˜bâ€™ and their respective magnitudes. Remember the notations â€˜iâ€™ and â€˜jâ€™ represent the spatial direction of the paths.
aâˆ™b = (a$_1$b$_1$) + (a$_2$b$_2$) (5)
a = âˆš(a$_1^2$ + a$_2^2$) (6)
b = âˆš(b$_1^2$ + b$_2^2$) (7)
If the directional paths â€˜xâ€™ and â€˜yâ€™ 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 â€˜xâ€™ and â€˜yâ€™ by making Î¸ the subject of the formula in equation (2).
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