The distance between the points (cosθ, sinθ) and (-sinθ, cosθ) is�

1.	The distance between the points (cosθ, sinθ) and (-sinθ, cosθ) is A) 1 B) √2 C) 2 D) √3
Answer» Correct option is (B) √2 Distance between points \(A(cos\,\theta,sin\,\theta)\;and\;B(-sin\,\theta,cos\,\theta)\) is \(AB=\sqrt{(-sin\,\theta-cos\,\theta)^2+(cos\,\theta-sin\,\theta)^2}\) \(=\sqrt{sin^2\,\theta+cos^2\,\theta+2\;sin\,\theta\,cos\,\theta+cos^2\,\theta\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+sin^2\,\theta-2\;sin\,\theta\,cos\,\theta}\) \(=\sqrt{2(sin^2\,\theta+cos^2\,\theta)}\) \(=\sqrt{2\times1}\) \((\because sin^2\,\theta+cos^2\,\theta=1)\) \(=\sqrt{2}\) units Correct option is B) √2

The distance between the points (cosθ, sinθ) and (-sinθ, cosθ) is A) 1 B) √2 C) 2 D) √3

Answer»

Correct option is (B) √2

Distance between points \(A(cos\,\theta,sin\,\theta)\;and\;B(-sin\,\theta,cos\,\theta)\) is \(AB=\sqrt{(-sin\,\theta-cos\,\theta)^2+(cos\,\theta-sin\,\theta)^2}\)

\(=\sqrt{sin^2\,\theta+cos^2\,\theta+2\;sin\,\theta\,cos\,\theta+cos^2\,\theta\\\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;+sin^2\,\theta-2\;sin\,\theta\,cos\,\theta}\)

\(=\sqrt{2(sin^2\,\theta+cos^2\,\theta)}\)

\(=\sqrt{2\times1}\) \((\because sin^2\,\theta+cos^2\,\theta=1)\)

\(=\sqrt{2}\) units

Correct option is B) √2

Discussion

No Comment Found

Related InterviewSolutions

If the points A(1, 2), B(2, 4) and C(3, a) are collinear, what is the length of BC ?(a) √2 units (b) √3 units (c) √5 units (d) 5 units
The two vertices of a triangle are (2, –1), (3, 2) and the third vertex lies on the line x + y = 5. The area of the triangle is 4 units. The third vertex is(a) (0, 5) or (1, 4) (b) (5, 0) or (4, 1) (c) (5, 0) or (1, 4) (d) (0, 5) or (4, 1)
The mid-point of the line joining the points (–10, 8) and (–6, 12) divides the line joining the points (4, –2) and (– 2, 4) in the ratio(a) 1 : 2 internally (b) 1 : 2 externally (c) 2 : 1 internally (d) 2 : 1 externally
The mid point of a line segment divides in the ratio A) 2 : 1 B) 1 : 2 C) 1 : 1 D) 8 : 7
The distance of the point P(-6,8) from the origin is(a) 8(b) 2√7(c) 6(d) 10
Find the points on the x–axis which are at a distance of 2√5 from the point (7, –4). How many such points are there?
The distance between the points (0, 5) and (–5, 0) is(A) 5 (B) 5√2 (C) 2√5 (D) 10
If points (1, 2), (-1, x) and (2, 3) are collinear, then x will be :(A) 2(B) 0(C) -1(D) 1
In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flowerpots have been placed at a distance of 1 m from each other along AD, as shown in given figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th distance AD on the eighth line and posts a red flag1. Find the position of green flaga) (2,25)b) (2,0.25)c) (25,2)d) (0, -25)2. Find the position of red flaga) (8,0)b) (20,8)c) (8,20)d) (8,0.2)3. What is the distance between both the flags? a).√41b) √11c) √61d) √514. If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?a) (5, 22.5)b) (10,22)c) (2,8.5)d) (2.5,20)5. If Joy has to post a flag at one-fourth distance from green flag ,in the line segment joining the green and red flags, then where should he post his flag?a) (3.5,24)b) (0.5,12.5)c) (2.25,8.5)d) (25,20)
The point (-2,-1), (1,0), (4,3) and (1,2) are the vertices of a : (A) Rectangle (B) Parallelogram (C) Square (D) Rhombus