If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
2x + y - 3z + 6 = 0
2x - y + 3z -14 = 0
2x - y + 3z - 13 = 0
2z + y + 3z - 10 = 0
The correct option is (B) 2x - y + 3z -14 = 0
If A is a square matrix of order 3, then |Adj(Adj A2)| =
Match the following List -I (Complex) List II (Spin only Magnetic Moment)
List -I (Complex) | List II (Spin only Magnetic Moment) | ||
A) | [CoF6]3- | I) | 0 |
B) | [Co(C2O4)3]3- | II) | √24 |
C) | [FeF6]3+ | III) | √8 |
D) | [Mn(CN)6]3- | IV) | √35 |
V) | √15 |
the correct answer is:
If (h,k) is the image of the point (3,4) with respect to the line 2x - 3y -5 = 0 and (l,m) is the foot of the perpendicular from (h,k) on the line 3x + 2y + 12 = 0, then lh + mk + 1 = 2x - 3y - 5 = 0.
If a line ax + 2y = k forms a triangle of area 3 sq.units with the coordinate axis and is perpendicular to the line 2x - 3y + 7 = 0, then the product of all the possible values of k is
The inverses of exponential functions are the logarithmic functions. The exponential function is y = ax and its inverse is x = ay. The logarithmic function y = logax is derived as the equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, (where, a > 0, and a≠1). In totality, it is called the logarithmic function with base a.
The domain of a logarithmic function is real numbers greater than 0, and the range is real numbers. The graph of y = logax is symmetrical to the graph of y = ax w.r.t. the line y = x. This relationship is true for any of the exponential functions and their inverse.
Exponential functions have the formation as:
f(x)=bx
where,
b = the base
x = the exponent (or power)