What is the vector u if u*v=12, u*w=14, v=6i+3j, w=2i+j ?

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Let the vector u be ai + bj.

u*v = (ai + bj)(6i + 3j) = 6a + 3b = 12

u*w = (ai + bj)(2i + j) = 2a + b = 14

Solve the simultaneous equations

6a + 3b = 12 and 2a + b = 14

We...

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Let the vector u be ai + bj.

u*v = (ai + bj)(6i + 3j) = 6a + 3b = 12

u*w = (ai + bj)(2i + j) = 2a + b = 14

Solve the simultaneous equations

6a + 3b = 12 and 2a + b = 14

We see that the system has no solutions as 6a + 3b = 12

=> 2a + b = 6

but 2a + b = 14

Therefore it is not possible to find a vector u which satisfies the given constraints.

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