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

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