Question: If E = (x, y, z) and F = (2, 3, 4) such that E · F = 10, what is the equation relating x, y, z?
Options:
2x + 3y + 4z = 10
x + y + z = 10
x + 2y + 3z = 10
2x + 3y + z = 10
Correct Answer: 2x + 3y + 4z = 10
Solution:
E · F = x*2 + y*3 + z*4 = 10 gives the equation 2x + 3y + 4z = 10.
If E = (x, y, z) and F = (2, 3, 4) such that E · F = 10, what is the equation re
Practice Questions
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
Questions & Step-by-Step Solutions
If E = (x, y, z) and F = (2, 3, 4) such that E · F = 10, what is the equation relating x, y, z?
Correct Answer: 2x + 3y + 4z = 10
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.
Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
Linear Equation – The result of the dot product can be expressed as a linear equation in terms of the variables involved.
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