If the position vector of point P is given by r = 3i + 4j, what is the distance

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Question: If the position vector of point P is given by r = 3i + 4j, what is the distance of point P from the origin?

Options:

Correct Answer: 5

Solution:

Distance = |r| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

If the position vector of point P is given by r = 3i + 4j, what is the distance of point P from the origin?

If the position vector of point P is given by r = 3i + 4j, what is the distance of point P from the origin?

Step 1: Identify the position vector of point P, which is given as r = 3i + 4j.
Step 2: Understand that the distance from the origin to point P can be found using the formula for the magnitude of the vector.
Step 3: The formula for the magnitude (or distance) of a vector r = ai + bj is |r| = √(a^2 + b^2).
Step 4: In our case, a = 3 and b = 4.
Step 5: Substitute the values into the formula: |r| = √(3^2 + 4^2).
Step 6: Calculate 3^2, which is 9, and 4^2, which is 16.
Step 7: Add the results: 9 + 16 = 25.
Step 8: Take the square root of 25: √25 = 5.
Step 9: Conclude that the distance of point P from the origin is 5.

Position Vector – Understanding the representation of a point in space using a vector.
Distance Calculation – Applying the Pythagorean theorem to find the distance from the origin in a 2D coordinate system.