If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector

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Question: If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?

Options:

Correct Answer: (2, 2)

Solution:

Vector PQ = Q - P = (1 - 3, 2 - 4) = (-2, -2).

If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?

If the position vector of point P is (3, 4) and Q is (1, 2), what is the vector PQ?

Step 1: Identify the position vector of point P, which is (3, 4).
Step 2: Identify the position vector of point Q, which is (1, 2).
Step 3: To find vector PQ, we need to subtract the coordinates of point P from the coordinates of point Q.
Step 4: Write the subtraction as Q - P, which means (1, 2) - (3, 4).
Step 5: Perform the subtraction for the x-coordinates: 1 - 3 = -2.
Step 6: Perform the subtraction for the y-coordinates: 2 - 4 = -2.
Step 7: Combine the results from Step 5 and Step 6 to get the vector PQ, which is (-2, -2).

Vector Subtraction – Understanding how to find the vector from one point to another by subtracting their position vectors.