Question

Ab and ac are 2 sides of triangle , find length of median through a

Answer 1

ABC is the triangle, AD is medium, AB=i+j, AC=3i+j-4k or BA=-i-j

CA+AB=CB (SUM of two side of a triangle equal to the other as per vector algebra)

Or -3i-j-4k+i+j=CB Or, -2i -4k =CB now CD=1/2 CB=-i-2k

Now in the triangle ACD, AC+CD=DA , OR 3i+j-4k-i-2k=DA OR, DA= 2i+j-2k

So length of medium= sqrt(2^2+1^2+2^2)= root(9)=3, minus value is ignored for length.