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Question

Consider the point   then

Solution

Correct option is

P, Q, R are non-collinear.

 and consider the determinant

                

Using R3 → R3 – cos θ R2 – sin θ R1

                

                  

                 

                  

Thus Δ ≠ 0 and t5he points P, Q, R are non-collinear.

SIMILAR QUESTIONS

Q1

Coordinate (x, y) of a point P satisfy the relation 3x + 4= 9, y = mx + 1. The number of integral value of m for which the x-coordinate of p is also an integer is

Q2

The point A(2, 3), B(3, 5), C(7, 7) and D(4, 5) are such that 

Q3

Q, R and are the points on the line joining the points P(a, x) and T(b, y) such that PQ = QR = RS = ST.

Q4

The line joining A(bcos α, bsin α) and B(acos β, asin β) is produced to point M(x, y) so that AM : MB = b : a, then 

Q5

OPQR is square and M, N are the middle points of the sides PQ and QRrespectively then the ratio of the areas of the square and the triangle OMNis

Q6

If px1x2….xi,….and q y1y2,…y… are in A.P. with common difference a and b respectively, then locus of the center of mean position of the point Ai (xi, yi), = 1, 2 …n is

Q7

If α, β, γ are the real roots of the equation x3 – 3px3 + 3qx – 1 = 0, then the centroid of the triangle with vertices 

Q8

The number of points (p, q) such that p, q Ïµ {1, 2, 3, 4} and the equation px2 + qx + 1 = 0 has real roots is

Q9

If G is the centroid and I the incentre of the triangle with vertices A(–36, 7), B(20, 7) and C(0, –8), then GI is equal to

Q10

A variable straight line of slope 4 intersects the hyperbola xy = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is