You visited us 1 times! Enjoying our articles? Unlock Full Access!

Addition of Vectors

Let ABC be ...

Question

Let $A B C$ be a triangle whose centroid is $G$ , orthocentre is $H$ and circumcentre is the origin ' $O$ '. If $D$ is any point in the plane of the triangle such that no three of $O, A, C$ and $D$ are collinear satisfying the relation $\to A D + \to B D + \to C H + 3 \to H G = λ \to H D$ , then what is the value of the scalar $^{'} λ^{'}$ ?

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2$
We know that in vector
$\to A B = \to O B - \to O A$ where O is the origin
SO from ques
$\to A D + \to B D + \to C H + 3 \to H G = λ \to H D$
$\to O D - \to O A + \to O D - \to O B + \to O H - \to O C + 3 \to O G - 3 \to O H = λ \to H D$
$2 \to O D - 2 \to O H - \to O A - \to O B - \to O C + 3 \to O G = λ \to H D$
$2 (\to O D - \to O H) - \to O A - \to O B - \to O C + 3 \to O G = λ \to H D$
$2 \to H D - \to O A - \to O B - \to O C + 3 \to O G = λ \to H D$
Comparing both sides
$λ = 2$

Suggest Corrections

Similar questions

A B C

G

H

O

D

O, A, C

D

- - \to A D + - - \to B D + - - \to C H + 3 - - \to H G = λ - - \to H D

λ

O, G

H

A B C

△ A B C

R = 3

O

H

\frac{1}{64} (A H^{2} + B C^{2}) (B H^{2} + A C^{2}) (C H^{2} + A B^{2})

3^{k}

k

∠

Join BYJU'S Learning Program