If E = (x, y, z) and F = (2, 3, 4) such that E · F = 10, what is the equation relating x, y, z?
Practice Questions
1 question
Q1
If E = (x, y, z) and F = (2, 3, 4) such that E · F = 10, what is the equation relating x, y, z?
2x + 3y + 4z = 10
x + y + z = 10
x + 2y + 3z = 10
2x + 3y + z = 10
E · F = x*2 + y*3 + z*4 = 10 gives the equation 2x + 3y + 4z = 10.
Questions & Step-by-step Solutions
1 item
Q
Q: If E = (x, y, z) and F = (2, 3, 4) such that E · F = 10, what is the equation relating x, y, z?
Solution: E · F = x*2 + y*3 + z*4 = 10 gives the equation 2x + 3y + 4z = 10.
Steps: 5
Step 1: Identify the vectors E and F. E is represented as (x, y, z) and F is given as (2, 3, 4).
Step 2: Understand that the dot product E · F is calculated by multiplying corresponding components of the vectors and then adding those products together.
Step 3: Write the formula for the dot product: E · F = x * 2 + y * 3 + z * 4.
Step 4: Set the dot product equal to the given value, which is 10: x * 2 + y * 3 + z * 4 = 10.
Step 5: Rewrite the equation in a simpler form: 2x + 3y + 4z = 10.
