Final answer:
The projection of vector u onto vector v, proj_v u, is found using the scalar component from the dot product of u and v divided by the magnitude of v squared. However, none of the provided options correctly match the result of the calculation 117/193, which suggests 'None of the above' would be the correct answer.
Step-by-step explanation:
The question asks for the projection of vector u onto vector v, which can be found using the formula for the projection of one vector onto another. The projection formula is projvu = (u · v / |v|2)v. Here, 'u · v' represents the dot product of u and v, and '|v|' is the magnitude of vector v.
First, we find the dot product of u and v:
u · v = (-8i - 3j) · (-12i - 7j) = 96 + 21 = 117
Next, we calculate the magnitude of v squared:
|v|2 = (-12i - 7j) · (-12i - 7j) = 144 + 49 = 193
Now we use these values to find the projection of u onto v:
projvu = (117 / 193)v
Since we are looking for a scalar answer (options are scalar numbers), we need to calculate the dot product u · v divided by the magnitude of vector v, without multiplying by vector v in the end. The answer will be the scalar component of u in the direction of v. Therefore, the correct answer is the scalar 117 divided by the magnitude squared of v which is 193.
To find the projection of vector u onto vector v, we realize that the answer must be a scalar value that represents how much of u is in the direction of v. Unfortunately, none of the given options (a) -44, (b) -52, (c) -36, (d) -28 exactly matches the resultant scalar value of 117/193, therefore the answer would be not listed in the options, and could be mentioned as 'None of the above' if that was an option.