1.

Three points with position vectors a, b and c will be collinear, if there exist scalars x, y and z such that (where x + y + z = 0)

Answer»

X a + y b = z c
XA + yb + zc = 0
xa + yb + zc = 0
xa + yb = c

Solution :Let A, B and C be the POINTS with POSITION vectors a, b and c respectively. These points will be collinear, if
`AB = LAMBDA AC`
`implies b-a=lambda(c-a)`
`implies (lambda-1)a+b+(-lambda)c=0`
`implies xa+yb+zc=0`
where, `x = lambda - 1, y = 1, z = - lambda`
`implies xa + yb + zc = 0` such that
x + y + z = 0


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