Vector addition.

 

Homogeneous differential equations.

 

The vectors a=(3, x, -1), b =(2, 1, y) are mutually perp, |vec.a|=|vec. b|,find x and y.

 

Find the value of (102)^5 by binomial theorem.

 

Find the value of (5^(1/2) )^4

The sum of three numbers in geometric progression is 56. If we subtract 1, 7, 21 from these numbers in that order we obtain an arithmetic progression. Find these numbers. [ncert]

 

Prove that sum of 2+4+8+ - - - - +2^n= -2(1-2^n).

 Given that 2+4+8+- - - - +2^n

This expression is a geometrical progression (G.P) . 

Let 'a' be the first term and 'r' the common ratio. 

Here a=2 and r=4/2 =8/4 = - - - =2^n/2^(n-1)=2

Sum of n terms of a G.P; S_n=a(1-r^n)/(1-r).

=> S_n=2(1-2^n)/(1-2)

=> S_n= -2(1-2^n).

Hence the result proved.

The position vectors of the vertices of a triangle are 2i ̂-j ̂+k ̂,i ̂-3j ̂- 5k ̂ and 3i ̂-4j ̂-4k ̂. Prove that It is a right angled triangle. [isc2003]

 

Find the factors of a polynomial 4x^3+3x^2-9x+2.