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KatRina
2 months ago
15

Given that P = (-5, 5) and Q = (-13, 10), find the component form and magnitude of 2 vector PQ.

Mathematics
2 answers:
tester [12.3K]2 months ago
4 0
Define the unit vectors along the x and y axes as \hat{i}, \, \hat{j} correspondingly.

Consequently, the vector from P to Q is
\vec{PQ} = (-13+5)\hat{i} + (10-5)\hat{j} = -8\hat{i} + 5\hat{j}
In terms of components, vector PQ is represented as (-8,5).

The magnitude of vector PQ can be calculated as
√[(-8)² + 5²] = √(89) = 9.434

Answer:
Thus, vector PQ is (-8, 5), and its magnitude equals √89 (or 9.434).
AnnZ [12.3K]2 months ago
3 0

Answer:

<-16, 10>, square root of 178

Step-by-step clarification:

The other contributor was nearly accurate, but they neglected to multiply their results by 2 and made a couple of errors in calculation.

To find PQ, you use the formula <q1-p1,q2-p2> (Remember, if asked for QP, simply switch to <p1-q1,p2-q2>)

-13 - (-5) = -8

10 - 5 = 5

Doubling these gives <-16,10>

To calculate the magnitude, apply the same formula as initially described: square each component, sum them, and then take the square root.

-13 - (-5) = -8

-8^2 = 64

10 - 5 = 5

5^2 = 25

64 + 25 = 89

89 * 2 = 178

Finally, take the square root: (square root of 178)

And you are finished!

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