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

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

Options:

Correct Answer: (-2, 6)

Solution:

Vector PQ = Q - P = (1 - 3, 4 - (-2)) = (-2, 6).

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

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

Step 1: Identify the position vector of point P, which is (3, -2).
Step 2: Identify the position vector of point Q, which is (1, 4).
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 for the x-coordinates: 1 (from Q) - 3 (from P).
Step 5: Calculate the x-coordinate: 1 - 3 = -2.
Step 6: Write the subtraction for the y-coordinates: 4 (from Q) - (-2) (from P).
Step 7: Calculate the y-coordinate: 4 - (-2) = 4 + 2 = 6.
Step 8: Combine the results from Step 5 and Step 7 to get vector PQ: (-2, 6).

Vector Subtraction – Understanding how to find the vector from one point to another by subtracting their position vectors.
Coordinate System – Knowledge of how to interpret and manipulate coordinates in a Cartesian plane.