If the position vector of a point is (5, 12), what is its distance from the orig

₹0.0

Question: If the position vector of a point is (5, 12), what is its distance from the origin?

Options:

Correct Answer: 13

Solution:

Distance = √(5^2 + 12^2) = √(25 + 144) = √169 = 13

If the position vector of a point is (5, 12), what is its distance from the origin?

If the position vector of a point is (5, 12), what is its distance from the origin?

Step 1: Identify the position vector of the point, which is (5, 12).
Step 2: Recognize that the origin is the point (0, 0).
Step 3: Use the distance formula, which is Distance = √(x^2 + y^2), where (x, y) are the coordinates of the point.
Step 4: Substitute the values from the position vector into the formula: Distance = √(5^2 + 12^2).
Step 5: Calculate 5^2, which is 25.
Step 6: Calculate 12^2, which is 144.
Step 7: Add the results from Step 5 and Step 6: 25 + 144 = 169.
Step 8: Take the square root of 169: √169 = 13.
Step 9: Conclude that the distance from the origin to the point (5, 12) is 13.

Distance Formula – The distance from a point (x, y) to the origin (0, 0) is calculated using the formula √(x² + y²).