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 ?
and . If || = 12, ||= 4√3 and . = 24 then which of the following is (are) true ? Options
A.
− |
| = 12
− || = 12B. − || = 30
− || = 30C.| × 
+ 
× 
| = 48√3
× + × | = 48√3D.. = − 72
. = − 72Solution
|
| = 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
.⇒
. = − 72Also by (1)
× 
= 
× 
⇒ |
× + × | = 2 | × |=
=
=
∴ A,C,D are correct & B incorrect
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