Let $$a = (-3, 3, 1)$$ $$b = (1, 4, -4)$$ $$c = (2, 1, -3)$$
For which values of $t \in \Re$ is $b + tc$ perpendicular to a?
For a vector to be perpendicular to $a$, the dot product of that vector and $a$ must equal to 0, right? I don't know where to go from here.
Also, can I do the following and in which case is there a solution and which case is impossible:
- $a \times (b.c)$
In the first case I am doing the cross product of a vector and a scalar and in the second case I am doing the dot product of a scalar and a vector, so I am not sure how that works.
For the first one, is this correct of $(-3, 3, 1)\times (18, 0, 0)$?