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The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, f
The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, find b and c.
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Q1
The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, find b and c.
3, 4
4, 3
5, 2
2, 5
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A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.
Questions & Step-by-step Solutions
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Q: The scalar product of vectors A = (a, b, c) and B = (1, 2, 3) is 14. If a = 2, find b and c.
Solution:
A · B = 2*1 + b*2 + c*3 = 14. Thus, 2 + 2b + 3c = 14, leading to 2b + 3c = 12.
Steps: 7
Show Steps
Step 1: Identify the vectors A and B. A = (a, b, c) and B = (1, 2, 3).
Step 2: Substitute the value of a into vector A. Since a = 2, A becomes (2, b, c).
Step 3: Write the formula for the scalar product (dot product) of vectors A and B. The formula is A · B = 2*1 + b*2 + c*3.
Step 4: Substitute the known values into the formula. This gives us 2*1 + b*2 + c*3 = 14.
Step 5: Calculate 2*1, which equals 2. Now the equation is 2 + 2b + 3c = 14.
Step 6: Simplify the equation by subtracting 2 from both sides. This gives us 2b + 3c = 12.
Step 7: Now we have a simplified equation, 2b + 3c = 12, which we can use to find values for b and c.
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