# Show that if P divides BC in the ratio 2:1 and Q divides CA in the ratio 1:3 then R divides AB in the ratio 3:2 externally.

Last updated date: 24th Mar 2023

•

Total views: 309k

•

Views today: 6.85k

Answer

Verified

309k+ views

Hint: Apply section formula and solve this question.

Given that point P divides BC in the ratio 2:1 and Q divides CA in the ratio 1:3 and R divides AB externally in the ratio 3:2

So we will consider $\lambda = \frac{2}{1},\mu = \frac{1}{3}$ and let R divide AB in the ratio v:1

So,from section formula we can write this as equal to

$

\lambda \mu v = - 1 \\

\Rightarrow 2.\dfrac{1}{3}v = - 1\therefore v = \frac{{ - 3}}{2} \\

$

Sine, we got v=$\dfrac{{ - 3}}{2}$

Therefore, we can say that R divides AB externally in the ratio 3:2 as the value of $v = \dfrac{{ - 3}}{2}$

Note: Always apply the relevant section formula in accordance to the data which is given, here since we have been given with both internal and external division ,we have applied the respective formula and solved it

Given that point P divides BC in the ratio 2:1 and Q divides CA in the ratio 1:3 and R divides AB externally in the ratio 3:2

So we will consider $\lambda = \frac{2}{1},\mu = \frac{1}{3}$ and let R divide AB in the ratio v:1

So,from section formula we can write this as equal to

$

\lambda \mu v = - 1 \\

\Rightarrow 2.\dfrac{1}{3}v = - 1\therefore v = \frac{{ - 3}}{2} \\

$

Sine, we got v=$\dfrac{{ - 3}}{2}$

Therefore, we can say that R divides AB externally in the ratio 3:2 as the value of $v = \dfrac{{ - 3}}{2}$

Note: Always apply the relevant section formula in accordance to the data which is given, here since we have been given with both internal and external division ,we have applied the respective formula and solved it

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?