Home
Class 12
MATHS
Let P ,Q ,R and S be the points on the p...

Let `P ,Q ,R` and `S` be the points on the plane with position vectors `-2i-j ,4i ,3i+3ja n d-3j+2j ,` respectively. The quadrilateral `P Q R S` must be a Parallelogram, which is neither a rhombus nor a rectangle Square Rectangle, but not a square Rhombus, but not a square

A

parallelogram which is neither a rhombus nor a rectangle

B

square

C

rectangle but not a square

D

rhombus but not a square

Text Solution

Verified by Experts

The correct Answer is:
A
`m_(PQ) =(1)/(6), m_(SR) =(1)/(6) , m_(RQ) =- 3 m_(SP) =- 3`

`rArr ` Parallelogram but neither PR= SQ nor PR `bot` SQ
`:. ` so it is a parallelogram which is neither a rhombus or a rectangle,
Promotional Banner

Similar Questions

Explore conceptually related problems

If the points with position vectors 60 hat i+2 hat j , 40 hat i-8 hat ja n da hat i-52 hat j are collinear, find the value of adot

ABCD is a rectangle and P,R and S are the mid - points of the AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

The points with position vectors 60 i+3j ,40 i-8j ,a i-52 j are collinear if a. a=-40 b. a=40 c. a=20 d. none of these

If the position vectors of P and Q are i + 3j - 7k and 5i - 2j + 4k then the cosine of the angle between PQ and y - axis is

Find the equation of the sphere described on the joint of points Aa n dB having position vectors 2 hat i+6 hat j-7 hat ka n d-2 hat i+4 hat j-3 hat k , respectively, as the diameter. Find the center and the radius of the sphere.

PQRS is a rectangle formed by joining the points P(-1, -1), Q(-1, 4), R(5,4) and S(5, -1) . A, B, C and D are the mid points of PQ, QR, RS and SR respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

O P Q R is a square and M ,N are the middle points of the sides P Qa n dQ R , respectively. Then the ratio of the area of the square to that of triangle O M N is (a)4:1 (b) 2:1 (c) 8:3 (d) 7:3

O P Q R is a square and M ,N are the midpoints of the sides P Q and Q R , respectively. If the ratio of the area of the square to that of triangle O M N is lambda:6, then lambda/4 is equal to (a)2 (b) 4 (c) 2 (d) 16

ABCD is a rectangle with A as the origin. vec b and vec d are the position vectors of B and D respectively. (i) What is the position vector of C? (ii) If P, Q, R and S are midpoints of sides of AB, BC, CD and DA respectively, find the position vector of P, Q, R,S,