Can someone help me find the answer to this question?
Three lines which form a triangle have vector equations:
$$r=16i-4j-6k+\lambda(-12i+4j+3k)$$
$$r=16i+28j+15k+\mu(8i+8j+5k)$$
$$r=i+9j+3k+v(4i-12j-8k)$$
Find the position vector of each of the three vertices of the triangle, given that the triangle formed is an acute angled triangle.
Can anybody tell me what the answer for the three position vectors are?
Best Answer
Once you have found the three vertices, in order to check the result, let plug the pair of values you have found for $\lambda$, $\mu$ and $\nu$ in the corresponding pair of equations.
As an alternative quick check the direction vector for any pair of vertices should be parallel to the direcion vector of the line passing through them.