If the position vector of a point P is (2, 3, 4), what is the distance from the

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Question: If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?

Options:

Correct Answer: 6

Solution:

Distance = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29 ≈ 5.385.

If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?

If the position vector of a point P is (2, 3, 4), what is the distance from the origin to point P?

Step 1: Identify the position vector of point P, which is (2, 3, 4).
Step 2: Recognize that the distance from the origin (0, 0, 0) to point P can be calculated using the distance formula in 3D space.
Step 3: Use the distance formula: Distance = √(x^2 + y^2 + z^2), where (x, y, z) are the coordinates of point P.
Step 4: Substitute the values from the position vector into the formula: Distance = √(2^2 + 3^2 + 4^2).
Step 5: Calculate each square: 2^2 = 4, 3^2 = 9, and 4^2 = 16.
Step 6: Add the squared values together: 4 + 9 + 16 = 29.
Step 7: Take the square root of the sum: Distance = √29.
Step 8: Approximate the square root: √29 ≈ 5.385.

Distance Formula in 3D – The distance from the origin to a point in 3D space is calculated using the formula √(x^2 + y^2 + z^2), where (x, y, z) are the coordinates of the point.