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If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?

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Question: If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?

Options:

  1. -10
  2. 10
  3. 0
  4. 6

Correct Answer: -10

Solution: 

C · D = 3*0 + (-2)*4 + 1*(-3) = 0 - 8 - 3 = -11.

If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?

Practice Questions

Q1
If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?
  1. -10
  2. 10
  3. 0
  4. 6

Questions & Step-by-Step Solutions

If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?
Correct Answer: -11
  • Step 1: Identify the coordinates of points C and D. C = (3, -2, 1) and D = (0, 4, -3).
  • Step 2: Write down the formula for the dot product: C · D = C1*D1 + C2*D2 + C3*D3.
  • Step 3: Substitute the values from C and D into the formula: C · D = 3*0 + (-2)*4 + 1*(-3).
  • Step 4: Calculate each term: 3*0 = 0, (-2)*4 = -8, and 1*(-3) = -3.
  • Step 5: Add the results of the calculations together: 0 + (-8) + (-3).
  • Step 6: Simplify the addition: 0 - 8 - 3 = -11.
  • Dot Product – The dot product of two vectors is calculated by multiplying their corresponding components and summing the results.
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