If and are two unit vectors such that + is also a unit vector, then find the angle between and
The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?
Show that the relation S in the set R of real numbers defined as S = {(a, b) : a, b ∈ R and a ≤ b³} is neither reflexive nor symmetric nor transitive.
Find the particular solution of the following differential equation :
y = 0, when x = 2.
Find the position vector of a point R, which divides the line joining two points P and Q whose position vectors are and respectively, externally in the ratio 1 : 2 Also, show that P is the mid-point, of line segment RQ.
The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x) = 3x² + 36x + 5, find the marginal revenue, when x = 5.
Find the equation(s) of the tangent(s) to the curve y = (x³ – 1) (x – 2) points where the curve intersects the x-axis.