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If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?
If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?
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Q1
If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?
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C · D = 3*0 + (-2)*4 + 1*(-3) = 0 - 8 - 3 = -11.
Questions & Step-by-step Solutions
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Q
Q: If C = (3, -2, 1) and D = (0, 4, -3), what is the value of C · D?
Solution:
C · D = 3*0 + (-2)*4 + 1*(-3) = 0 - 8 - 3 = -11.
Steps: 6
Show Steps
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.
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