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

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Question: If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-coordinate of point P? (2020)

Options:

Correct Answer: 2

Exam Year: 2020

Solution:

The x-coordinate of point P is the coefficient of i in the position vector, which is 2.

If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-coordinate of point P? (2020)

If the position vector of point P is given by r = 2i + 3j + 4k, what is the x-coordinate of point P? (2020)

Step 1: Identify the position vector given in the question, which is r = 2i + 3j + 4k.
Step 2: Understand that the position vector is made up of three components: the x-component (i), the y-component (j), and the z-component (k).
Step 3: Look for the coefficient of 'i' in the position vector, as this represents the x-coordinate.
Step 4: In the position vector r = 2i + 3j + 4k, the coefficient of 'i' is 2.
Step 5: Conclude that the x-coordinate of point P is 2.

Position Vectors – Understanding that a position vector is expressed in terms of its components along the x, y, and z axes, represented by i, j, and k respectively.
Coordinate Extraction – Identifying specific coordinates from a vector representation, particularly the x-coordinate from the i component.