Home
Class 12
MATHS
Statement I: If a=2hati+hatk,b=3hatj+4ha...

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).

A

Statement-I and statement II ar correct and Statement II is the correct explanation of statement I

B

Both statement I and statement II are correct but statement II is not the correct explanation of statement I

C

Statement I is correct but statement II is incorrect

D

Statement II is correct but statement I is incorrect

Text Solution

Verified by Experts

The correct Answer is:
B
a,b and c are coplanar `c=lamda a+mubimplieslamda=4 and mu=-1`.
Promotional Banner

Similar Questions

Explore conceptually related problems

What does a_(1) + a_(2) + a_(3) + …..+ a_(n) represent

Find the relation between acceleration of blocks a_(1), a_(2) and a_(3) .

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1), a_(2), a_(3).,,,,,,,,a_(n) are in A.P and their common difference is d. The value of the series sin d_(1) [sec a_(1).sec a_(2) + sec a_(2).sec a_(3)+ ….+ sec a_(n-1).sec a_(n)] is……..

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1),a_(2),a_(3),a_(4) and a_(5) are in AP with common difference ne 0, find the value of sum_(i=1)^(5)a_(i) " when " a_(3)=2 .

If a_(1),a_(2),a_(3),"….",a_(n) are in AP, where a_(i)gt0 for all I, the value of (1)/(sqrta_(1)+sqrta_(2))+(1)/(sqrta_(2)+sqrta_(3))+"....."+(1)/(sqrta_(n-1)+sqrta_(n)) is

Differentiate a_(0)x^(n)+a_(1)x^(n-1)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n)

Statement I: a=hati+phatj+2hatk and b=2hati+3hatj+qhatk are parallel vectors, iff p=(3)/(2) and q=4 . Statement II: a=a_(1)hati+a_(2)hatj+a_(3)hatk and b=b_(1)hati+b_(2)hatj+b_(3)hatk are parallel (a_(1))/(b_(1))=(a_(2))/(b_(2))=(a_(3))/(b_(3)) .

If a_(1), a_(2), a_(3),……,a_(n) are in AP, where a_(i) gt 0 for all i, show that (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3))) + …..+ (1)/(sqrt(a_(n-1))+ sqrt(a_(n)))= (n-1)/(sqrt(a_(1)) + sqrt(a_(n)))