Two vectors A and B are given by A = 4i + 8j and B = 6i – 2j. The scalar product of A and a third vector C is –16. The scalar product of B and C is +18. The z component of C is 0. What is the magnitude of C?
Vector magnitude?
Let C = ai + bj + ck. As stated in the problem, c = 0; therefore, C = ai + bj.
A • C = 4a + 8b = −16
B • C = 6a − 2b = 18
Solving this system, a = 2, b = −3.
| C | = √ (2² + 3²) = √13.
Check:
A • C = (4i + 8j) • (2i − 3j) = 4 × 2 + 8 × -3 = −16.
B • C = (6i − 2j) • (2i − 3j) = 6 × 2 + -2 × -3 = 18.
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