Home
Class 12
MATHS
If the segments joining the points A(a ,...

If the segments joining the points `A(a , b)a n d\ B(c , d)` subtends an angle `theta` at the origin, prove that : `theta=(a c+b d)/((a^2+b^2)(c^2+d^2))`

Text Solution

Verified by Experts

The correct Answer is:
`OA. OB cos theta = ac + bd`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|1 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise For Session 1|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|20 Videos

  • DEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|37 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the solutions of a cos theta+b sin theta=c , then prove that : cos (alpha- beta)= (2c^2- (a^2+b^2))/(a^2+b^2) .

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

If acos theta-b sin theta=c , show that asin theta+b cos theta=+-sqrt(a^2+b^2-c^2dot)

Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

If x-iy= sqrt((a-ib)/(c-id)) , prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^2) .

If x-iy= sqrt((a-ib)/(c-id)) prove that (x^2+y^2)^2= (a^2+b^2)/(c^2+d^2) .

If a, b, c, d are in G.P, prove that (a^n + b^n), (b^n + c^n), (c^n + d^n) are in G.P.

Prove that [axxb, a xx c, d] = (a*d)[a, b, c]

If x = a cos theta + b sin theta and y =asin theta-b cos theta , then prove that y^2 (d^2y)/(dx^2)-x(dy)/(dx)+y=0

If vec a+ vec b+ vec c= 0 , show that the angle theta between vec a and vec b is given by cos theta = c^2- a^2- b^2 / 2ab .