JEE Advanced | 2015Properties of TriangleHard

Question

Let ᐃPQR be a triangle. Let and . If || = 12, ||= 4√3 and . = 24 then which of the following is (are) true ?

Options

A. − || = 12
B. − || = 30
C.| × + × | = 48√3
D.. = − 72

Solution

                                            
|| = 12, || = 4√3
+ + = 0            .......(1)
a2 = b2 + c2 + 2.
144 = 48 + c2 + 48
c2 = 48 ⇒ c = 4√3
Also c2 = a2 + b2 + 2.
48 = 144 + 48 + 2.
⇒ . = − 72
Also by (1)
× = ×
⇒ | × + × | = 2 | × |
=
=
=
∴ A,C,D are correct & B incorrect

Create a free account to view solution

View Solution Free
Topic: Properties of Triangle·Practice all Properties of Triangle questions

More Properties of Triangle Questions

In a triangle ABC, (a + b + c) (b + c − a) = λbc if -...Two lines are drawn through (3, 4), each of which makes angle of 45o with the line x - y = 2, Then area of the triangle ...In a ᐃABC, if A = 30o, b = 2, c = √3, then =...The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0...In a triangle ABC, let ∠C = If r is the inradius and R is the circumradius of the the triangle ABC, then 2 (r + R)...