CHECK THE POINTS ARE VERTICES OF ISOSCELES TRIANGLE IN VECTOR

About "Check the Points are Vertices of Isosceles Triangle in Vector"

Check the Points are Vertices of Isosceles Triangle in Vector

Here we are going to see how to check the points are vertices of isosceles triangle in vector.

Check the Points are Vertices of Isosceles Triangle in Vector - Practice Question

Question 1 :

Show that the points A (1, 1, 1), B(1, 2, 3) and C(2, - 1, 1) are vertices of an isosceles triangle

Solution :

In an isosceles triangle length of two sides will be equal. 

OA vector  =  (i + j + k) vector

OB vector  =  (i + 2j + 3k) vector

OC vector  =  (2i - j + k) vector

AB vector  =  OB - OA

  =  (i + 2j + 3k) - (i + j + k)

  =  (j + 2k) vector

|AB|  =  √12 + 2=  √5

BC vector  =  OC - OB

  =  (2i - j + k)  -  (i + 2j + 3k) 

  =  (i - 3j - 2k) vector

|BC|  =  √12 + (-3)2(-2)2    =  √14

CA vector  =  OC - OB

  =  (2i - j + k) -  (i + j + k) 

  =  (i - 2j) vector

|CA|  =  √12 + (-2)2   =  √5

Sides AB and CA are equal. Hence the given points are the vertices of isosceles triangle.

Question 2 :

Find the value or values of m for which m (i + j + k) is a unit vector.

Solution :

a vector  =  mi vector + mj vector + mk vector

If the given is unit vector, then |a vector|  =  1

  √m2 + m+ m=  1

  √3m2  =  1

m2  =  1/3

m  =  ±1/√3

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