If the points P- Q- R- S have position vectors p- q- r- s such that p - q - 2s - r- then find out the correct one-

The correct option is D PQ and PR trisect each otherWe have, p q=2(s r) ⇒ p+2r=q+2s⇒ #160; p+2r / 1+2 = q+2s / 1+2 ∴ Point divid ...

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

Byju's Answer

Standard XII

Mathematics

Section Formula

If the points...

Question

If the points $P, Q, R, S$ have position vectors $\to p, \to q, \to r, \to s$ such that $\to p - \to q = 2 (\to s - \to r)$ , then find out the correct one:

P Q

and

R S

bisect each other

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

P Q

and

P R

bisect each other

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

P Q

and

R S

trisect each other

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

P Q

and

P R

trisect each other

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

Open in App

Solution

The correct option is D $P Q$ and $P R$ trisect each other
We have, $p - q = 2 (s - r)$
$\Rightarrow p + 2 r = q + 2 s \Rightarrow \frac{p + 2 r}{1 + 2} = \frac{q + 2 s}{1 + 2}$
$∴$ Point dividing $P R$ in the ratio $2 : 1$ is same as the point dividing $Q S$ in the ratio $2 : 1$
Hence $Q S$ and $P R$ trisect each other.

Suggest Corrections

Similar questions

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

Q. The position vectors of

P

and

Q

are respectively

a

and

b

. If

R

is a point on

P Q

P Q

such that

P R = 5 P Q

, then the position vector of

R

If the points P , Q, R and S are collinear points and PQ=RS then prove that PR=QS using Euclid’s postulate.

Q. The position vectors of

P

and

Q

are respectively

a

and

b

. If

R

is a point on

- - \to P Q

such that

- - \to P R = 5 - - \to P Q

, then the position vector of

R

Q. Question 12
If S is a point on the side PQ of a

Δ

PQR such that PS = QS = RS, then

(A) (P R) (Q R) = R S^{2}

(B) Q S^{2} + R S^{2} = Q R^{2}

(C) P R^{2} + Q R^{2} = P Q^{2}

(D) P S^{2} + R S^{2} = P R^{2}

Join BYJU'S Learning Program

If the points P, Q, R, S have position vectors →p, →q, →r, →s such that →p−→q=2(→s−→r), then find out the correct one:

The correct option is D PQ and PR trisect each otherWe have, p−q=2(s−r)⇒p+2r=q+2s⇒p+2r1+2=q+2s1+2∴ Point dividing PR in the ratio 2:1 is same as the point dividing QS in the ratio 2:1Hence QS and PR trisect each other.

If the points $P, Q, R, S$ have position vectors $\to p, \to q, \to r, \to s$ such that $\to p - \to q = 2 (\to s - \to r)$ , then find out the correct one: