Show that the points A, B, C with position vectors 
, 
and 
respectively are the vertices of a right angled triangle. Also find the remaining angles of the triangle
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
∠ A = cos –1 
, ∠ B = cos –1 
, ∠ C = 
Solution : We have,
= 
– 
= 
= 
– 
= 
and, 
= 
– 
= 
Since 
+ 
+ 
= 
+ 
+ 
= 
So A, B and C are the vertices of a triangle.
Now, 
. 
= 
. 
= –2 – 3 + 5 = 0
⇒ 
⇒ ∠ BCA = 
⇒ ABC is a right angled triangle.
Since A is the angle between the vectors 
and 
. Therefore
cos A = 
= 
= 
= 
= 
⇒ A = cos –1 
cos B = 
= 
⇒ cos B = 
= 
⇒ B = cos –1 
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