Find the solutions to v in:
(-i + 2j + 3k) X v = i + 5j - 3k
I have tried this question multiple times using the method of solving three equations in 3 unknowns but keep going around in circles!
Any help would be very much appreciated!
The general solution is found by letting one of the unknowns equal a parameter. Eg. Let where t is any real number. Then:
If all you want is just one concrete solution, substitute a convenient value for t. t = 0 is pretty convenient ......
The initial question can also be answered using another method : Given two vectors and , (both different from ) we want to solve for .
_ If and aren't orthogonal, this equation has no solution.
_ If then has to be orthogonal to too. As and aren't collinear and are both orthogonal to , the solutions of (1) can be written for . If we put this in (1), we get
There is no condition on and the value of is . In your case, and which gives hence the solutions are
which happens to be Mr. Fantastic's solution.