1 if the vector -i+j-k bisect the angle b/w the vector c and the vector 3i+ 4j find the unit vector in the dirn of c explain in better way

2 prove pythagoras theorem by vector method angle a is right angle u have to explain step by step also prove that unit pt of hypotenuse is equidistant from vertices

Asked byKeshav Kr1 week, 4 days agoSubject:Math

1).

2).

Here ABC is a right triangle ,right angled at A.
Vector AB = x , Vector AC = y,
So hypotenuse BC = x + y ,  [ In a triangle ,a + b = c]
As AB and AC are perpendicular to each other, so x.y = 0  [ dot product = 0, for perpendicular vectors]

So |x + y|² = (x+y).(x+y)
= x.x + y.y + 2x.y
= |x|² + |y|²  (as x.x = |x|² ,and x.y = 0)
Hence this is the expression for Pythagoras theorem.