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.
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
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 + 22 = √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.
a vector = mi vector + mj vector + mk vector
If the given is unit vector, then |a vector| = 1
√m2 + m2 + m2 = 1
√3m2 = 1
m2 = 1/3
m = ±1/√3
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