सदिश विधि का प्रयोग करते हुए `lambda` व `mu` मन ज्ञात कीजिए यदि बिन्दु `(3, lambda, mu),(2,0,-3)` तथा `(1,-2,-5)` संरेख है।

Using the vector method , find the values of lambda " and " mu for which the points A(3, lambda ,mu) B(2,0,-2) " and " C(1,-2,-5) are collinear

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

Find the values of lambda ad mu if the points A(-1,4,-2),B(lambda,mu,1) and C(0,2,-1) are collinear.

The d.r's of two parallel lines are 4, - 3, -1 and lambda + mu, 1 + mu,2 . Then (lambda,mu) is

The cartesian equation of the plane whose vector equation is r = (1 + lambda - mu) i + (2 - lambda) j + (3- 2 lambda + 2mu)k , where lambda, mu are scalars, is

Find the shortest distance between the following (1-4) lines whose vector equations are : (i) vec(r) = (lambda - 1) hati + (lambda -1) hatj - (1 + lambda ) hatk and vec(r) = (1 - mu) hat(i) + (2 mu - 1) hatj + (mu + 2) hatk (ii) vec(r) = (1 + lambda) hati + (2 - lambda) hatj + (1 + lambda) hatk and vec(r) = 2 (1 + mu) hati - (1 - mu) hatj + (-1 + 2mu ) hatk .

If the greatest and least values of the function f(x)=arctan x-(1)/(2)ln x on [(1)/(sqrt(3)),sqrt(3)] are lambda and mu respectively. Then (A) [lambda +mu]=1 where [.]= greatest Integer function (B) (lambda +mu)=2 where (.)= least Integer function (C) (lambda+mu)=0 where (.)= least Integer function (D) [lambda +mu]=-1 where [.]= greatest Integer function

The value of (lambda, mu) for which (lambda - mu) x^3 - (lambda - 2) x^2 -3x +7=0 will have two infinite roots is

यदि A (-hati + 3hatj + 2hatk) , B (-4hati + 2hatj - 2hatk) तथा C(5hati + (lambda +1)hatj + mu hatk) संरेखीय है तब :