Gandalf the grey started in the forest of mirkwood at a point with coordinates (2,1)(2,1) and arrived in the iron hills at the point with coordinates (3,6)(3,6). if he began walking in the direction of the vector v¯¯¯=5i+1jv¯=5i+1j and changed direction only once, when he turned at a right angle, at what point did he make the turn?

Answer is x = -24/13,  y = 3/13

Step-by-step explanation:

The vector equation of line is;

(x,y) = () + t (v)  ...............  1

we know that;

() = (2,1)    

and

v = 5i + 1j

put in equation 1

The parametric equation becomes;

by comparison we get;

multiply equation 3 by -5 and add it to equation 2

we know that;

so, m = 5

we can find the family of lines that are perpendicular to the above line by swapping the coefficients and change the sign of one of them:

So, the equation of other line is

multiply equation 5 by -5

put this value of y in equation 5.

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step-by-step explanation: