If the position vector of point P is given by r = 2i + 3j + 4k, what is the dist

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Question: If the position vector of point P is given by r = 2i + 3j + 4k, what is the distance from the origin to point P?

Options:

Correct Answer: 6

Solution:

Distance = |r| = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29.

If the position vector of point P is given by r = 2i + 3j + 4k, what is the distance from the origin to point P?

If the position vector of point P is given by r = 2i + 3j + 4k, what is the distance from the origin to point P?

Step 1: Identify the position vector of point P, which is given as r = 2i + 3j + 4k.
Step 2: Understand that the distance from the origin to point P is represented by the magnitude of the position vector r.
Step 3: To find the magnitude, use the formula |r| = √(x^2 + y^2 + z^2), where x, y, and z are the coefficients of i, j, and k in the position vector.
Step 4: Substitute the values from the position vector into the formula: |r| = √(2^2 + 3^2 + 4^2).
Step 5: Calculate each square: 2^2 = 4, 3^2 = 9, and 4^2 = 16.
Step 6: Add these squared values together: 4 + 9 + 16 = 29.
Step 7: Take the square root of the sum: √29.
Step 8: The final result is the distance from the origin to point P, which is √29.

Position Vectors – Understanding how to interpret position vectors in three-dimensional space.
Distance Calculation – Applying the formula for the distance from the origin to a point represented by a position vector.
Square Root and Squaring – Performing operations involving squares and square roots correctly.