If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?
Practice Questions
1 question
Q1
If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?
-3i - 4j - 5k
3i + 4j + 5k
0
None of the above
The reflection of A in the plane x + y + z = 0 is -A = -3i - 4j - 5k.
Questions & Step-by-step Solutions
1 item
Q
Q: If the vector A = 3i + 4j + 5k is reflected in the plane x + y + z = 0, what is the reflected vector?
Solution: The reflection of A in the plane x + y + z = 0 is -A = -3i - 4j - 5k.
Steps: 6
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.
