If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is

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Question: If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?

Options:

Correct Answer: -3i - 4j - 5k

Solution:

The reflection of A in the plane x + y + z = 0 is -A = -3i - 4j - 5k.

If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?

If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?

Step 1: Identify the original vector A, which is given as A = 3i + 4j + 5k.
Step 2: Understand that reflecting a vector in a plane means finding a new vector that is on the opposite side of the plane.
Step 3: The plane is defined by the equation x + y + z = 0. This means that any point (x, y, z) on the plane satisfies this equation.
Step 4: To reflect the vector A in the plane, we need to find the negative of the vector A. This is done by changing the sign of each component of the vector.
Step 5: Calculate the negative of vector A: -A = -3i - 4j - 5k.
Step 6: The reflected vector is -3i - 4j - 5k, which is the final answer.

Vector Reflection – Understanding how to reflect a vector across a given plane using geometric principles.
Plane Equation – Recognizing the equation of a plane and how it relates to vector reflection.
Vector Components – Breaking down vectors into their components and understanding their geometric interpretation.