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!
See the note at the end of my edited first post.
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 ......
Hello
Given two vectors and , if a vector is a solution of then for all one has : every vector is also a solution of (1). That's why if there is one solution then there is an infinite number of solutions.
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.