Home
Class 12
MATHS
If a(1) and a(2) are two values of a for...

If `a_(1)` and `a_(2)` are two values of a for which the unit vector `aveci + bvecj +1/2veck` is linearly dependent with `veci+2vecj` and `vecj-2veck`, then `1/a_(1)+1/a_(2)` is equal to

A

(a)1

B

(b)`(1)/(8)`

C

(c)`(-16)/(11)`

D

(d)`(-11)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
C
`ahati+bhatj+(1)/(2)hatk=l(hati+2hatj)+m(hatj-2hatk)`
`implies a=l,b=2l+m and m=(-1)/(4)`
`ahati+bhatj+(1)/(2) hatk` is unit vector
`therefore a^(2)+b^(2)=(3)/(4)implies5a^(2)-a-(11)/(16)=0`
`a_(1) and a_(2)` are roots of above equation
`implies(1)/(a_(1))+(1)/(a_(2))=(a_(1)+a_(2))/(a_(1)a_(2))=-(16)/(11)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If a_(1)=2 and a_(n)=2a_(n-1)+5 for ngt1 , the value of sum_(r=2)^(5)a_(r) is

Statement I: If a=2hati+hatk,b=3hatj+4hatk and c=lamda a+mub are coplanar, then c=4a-b . Statement II: A set vector a_(1),a_(2),a_(3), . . ,a_(n) is said to be linearly independent, if every relation of the form l_(1)a_(1)+l_(2)a_(2)+l_(3)a_(3)+ . . .+l_(n)a_(n)=0 implies that l_(1)=l_(2)=l_(3)= . . .=l_(n)=0 (scalar).

If A_(1), A_(2) be two A.M's and G_(1), G_(2) be two G.M's between a and b , then (A_(1)+A_(2))/(G_(1) G_(2)) is equal to

Let (a_(1),b_(1)) and (a_(2),b_(2)) are the pair of real numbers such that 10,a,b,ab constitute an arithmetic progression. Then, the value of ((2a_(1)a_(2)+b_(1)b_(2))/(10)) is

If 1, a_(1), a_(2). ..., a_(n-1) are n roots of unity, then the value of (1 - a_(1)) (1 - a_(2)) .... (1 - a_(n-1)) is :

In a four-dimensional space where unit vectors along the axes are hati,hatj,hatk and hatl, and a_(1),a_(2),a_(3),a_(4) are four non-zero vectors such that no vector can be expressed as a linear combination of other (lamda-1) (a_(1)-a_(2))+mu(a_(2)+a_(3))+gamma(a_(3)+a_(4)-2a_(2))+a_(3)+deltaa_(4)=0 , then

If a_(1),a_(2),a_(3),a_(4) are coefficients of any four consecutive terms in the expansion of (1+x)^(n) , then (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4)) equals:

The area of a circle is A_(1) and the area of a regular pentagon inscribed in the circle is A_(2) . Then A_(1)//A_(2) is

If one geometric mean G and two arithmetic means A_(1) and A_(2) are inserted between two given quantities then, (2 A_(1)-A_(2))(2 A_(2)-A_(1))=

Write the first five terms of each of the sequences and obtain the corresponding series: a_(1) =a_(2) =2 , a_(n) =a_(n-1) -1, n gt 2