Consider three points `P = (-sin (beta-alpha), -cos beta)`, `Q = (cos(beta-alpha), sin beta)`, and `R = ((cos (beta - alpha + theta), sin (beta - theta))`, where `0< alpha, beta, theta < pi/4` ThenA. P lies on the line segmennt RQB. Q lies on the line segmet PRC. R lies on the line segment QPD. P,Q,R are non-colinear

Consider three points `P = (-sin (beta-alpha), -cos beta)`, `Q = (cos(

1.	Consider three points `P = (-sin (beta-alpha), -cos beta)`, `Q = (cos(beta-alpha), sin beta)`, and `R = ((cos (beta - alpha + theta), sin (beta - theta))`, where `0< alpha, beta, theta < pi/4` ThenA. P lies on the line segmennt RQB. Q lies on the line segmet PRC. R lies on the line segment QPD. P,Q,R are non-colinear
Answer» Correct Answer - D Let the coordinates of P and Q be `(x_(1),y_(1)) and (x_(2),y_(2))` respectively. Then `x_(1)=sin (beta-alpha), y_(1)=- cos beta, x_(2)= cos (beta-alpha),y_(2)= sin beta`. The coordinates of R are `(cos (beta-alpha+theta), sin (beta-theta))` , `or , (cos(beta-alpha)cos theta-sin theta(beta-alpha)sin theta, sin beta cos theta-cos beta sin theta)` `or (x_(1) sin theta+x_(2)cos, theta, y_(1)sin theta+y_(2) theta)` We observe that the poins having coordinates `((x_(1) sin theta+x_(2)cos theta)/(sin theta+ cos theta),(y_(1)sin theta+y_(2) cos theta)/(sin theta+cos theta))` divides PQ internally in the ratio `cos theta: sin theta` . So, P,Q S are coolinerr points. But P,Q R are non-Collinear.

Discussion

No Comment Found

Related InterviewSolutions

Find the incentre of the triangle with vertices `(1, sqrt3), (0, 0)` and `(2, 0)`A. `(1,sqrt(3)//2)`B. `(2//3,1,sqrt(3))`C. `(2//3,sqrt(3)//2)`D. `(1//1,sqrt(3))`
The coordinates of the point where origin is shifted is (-1,2) so that the equation`2x^(2)+y^(2)-4x+4y=0` become?A. `X^(2)+2Y^(2)=6`B. `2X^(2)+y^(2)=6`C. `2X^(2)+Y^(2)=4`D. `X^(2)+2Y^(2)=4`
Statement-1 : The points A(-2,2), B(2,-2) and C(1,1) are the vertices of an obtuse angled isoscles triangle. Statement-2: Every abtuse angle tirangle is isosceles.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1B. Statement-1 is True, Statement-2 is True, Statement-2 not a correct explanation for Statement-1C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True
If the vertices of a triangle `PQR` are rational points, then which of the following points of this triangle may not be rational -(a) Centroid (b) Incenter(c) Circumcenter (d) OrthocenterA. centroidB. incentreC. circumentreD. orthoentre
21. If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle isA. `((1)/(3),(7)/(3))`B. `(2,(7)/(3))`C. `(-(1)/(3),(7)/(3))`D. `(-1,(7)/(3))`
By shifting origin to `(-1,2)` the equation `y^2+8x - 4y + 12 = 0` changes as `Y^2 = 4aX` then `a=`A. 1B. 2C. `-2`D. `-1`
The area of the quadrilateral whose vertices are `(1,2)(6,2),(5,3) and (3,4)`, isA. `(3)/(2)` sq. unirtsB. `(11)/(2)` sq. unirtsC. `(1)/(2)` sq. unirtsD. none of these
If points `(a^2, 0),(0, b^2) and (1, 1)` are collinear, thenA. `(1)/(a^(2))+(1)/(b^(2))=1`B. `(1)/(a)+(1)/(b)=1`C. `a^(2)+b^(2)=1`D. none of these
If the coordinates of two points `A`and `B`are (3, 4)and `(5,-2)`, respectively, find the coordinates of any point `P`if `P A=P Bdot`Area of ` P A B`is 10 sq.units.A. (2,7)B. (7,2)C. (1,0)D. (0,1)
The angles A, B and C of a `DeltaABC` are in A.P. If `AB = 6, BC =7`,then `AC =`A. 5B. 7C. 8D. none of these

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment