MyQuestionIcon

1

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

Ratios of Distances between Centroid, Circumcenter, Incenter and Orthocenter of Triangle

Let ABC be a ...

Question

Let $A B C$ be a triangle whose circumcentre is at $P$ . If the position vectors of $A, B, C$ and $P$ are $\to a, \to b, \to c$ and $\frac{\to a + \to b + \to c}{4}$ respectively, then the position vector of the orthocentre of this trianlge, is:

A

\to a + \to b + \to c

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

B

\to 0

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

C

- (\frac{\to a + \to b + \to c}{2})

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

D

\frac{\to a + \to b + \to c}{2}

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

Open in App

Solution

The correct option is D $\frac{\to a + \to b + \to c}{2}$
Position vector of centroid of $△ A B C = \frac{\to a + \to b + \to c}{3}$
We know that orthocentre, centroid and circumcentre of any triangle are collinear and the centroid divides the line-segment joining orthocentre and circumcentre in the ratio $2 : 1$ .
$∴ \frac{\to a + \to b + \to c}{3} = \frac{2 (\frac{\to a + \to b + \to c}{4}) + 1 (P.V. of orthocentre)}{2 + 1}$
$\Rightarrow P.V. of orthocentre = \frac{\to a + \to b + \to c}{2}$

Suggest Corrections

thumbs-up

3

Similar questions

A B C

be a triangle whose circumcentre is at

P

. If the position vectors of

A, B, C

P

\to a, \to b, \to c

\frac{\to a + \to b + \to c}{4}

respectively, then the position vector of the orthocentre of this trianlge, is:

A B C

be a triangle whose circumcentre is at

P

. If the position vectors of

A, B, C

P

\to a, \to b, \to c

\frac{\to a + \to b + \to c}{4}

respectively, then the position vector of the orthocentre of this trianlge, is:

A B C

be a triangle whose circumcentre is at P. If the position vectors of

A, B, C

\to a, \to b, \to c

\frac{\to a + \to b + \to c}{4}

respectively, then the position vector of the orthocentre of this triangle, is:

A B C

be a triangle and

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

be the position vectors of the vertices

A, B, C

respectively, the internal bisectors of angle

C

and the external bisectors of

∠ A

∠ B

meet at a point

P

a, b, c

be the lengths of the sides

B C, C A

A B

respectively then position vector of point

P

C

referred to origin is

Q. Let ABC be a triangle and

\to a

\to b

\to c

be the position vectors of the point.

A, B

C,

respectively. External bisectors of

∠

a n d

C m e e t a t P w i t h t h e s i d e s o f t h e t r i a n g l e a s

a n d

t h e p o s i t i o n v e c t o r s o f

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Ratios of Distances between Centroid, Circumcenter, Incenter and Orthocenter of Triangle

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon