Question

Given F = <9, 7> and G = <6, -9>, find |F – G| and |F + G|, providing exact answers.

a) |F – G| = 13 and |F + G| = 15
b) |F – G| = 3 and |F + G| = 2
c) |F – G| = 12 and |F + G| = 14
d) |F – G| = 9 and |F + G| = 15

Answer 1

After performing vector subtraction and addition for vectors F and G, we find that |F - G| equals the square root of 265, and |F + G| equals the square root of 229, neither of which match the provided options.

Step-by-step explanation:

To find the vector |F − G| and |F + G| when given F = <9, 7> and G = <6, -9>, we need to perform vector subtraction and addition respectively, followed by finding the magnitude of the resultant vectors.

For |F − G|, we subtract the components of G from F:
F − G = <9 − 6, 7 − (-9)> = <3, 16>.

The magnitude of this resultant vector is calculated using the Pythagorean theorem:

|F − G| = √(32 + 162) = √(9 + 256) = √265.

To find the exact value, we can simplify √265:

|F − G| = √265 ≈ 16.28 (approx) but since the question asks for exact answers, we leave it as √265.

Now for |F + G|, we add components of F and G together:
F + G = <9 + 6, 7 + (-9)> = <15, -2>.

The magnitude of this resultant vector is:

|F + G| = √(152 + (-2)2) = √(225 + 4) = √229.

So, once again leaving the exact answer in radical form, we have |F + G| = √229.

Thus, none of the provided options (a, b, c, or d) match the correct magnitudes for |F − G| and |F + G|.