Home
Class 12
MATHS
If vec ais a nonzero vector of magnit...

If ` vec a`is a nonzero vector of magnitude a and `lambda`a nonzero scalar, then `lambda`` vec a`is unit vector if(A) `lambda = 1` (B) `lambda= -1` (C) `a = |lambda|` (D) `a = 1/(|lambda|)`

Text Solution

AI Generated Solution

To solve the problem, we need to determine under what conditions the vector \( \lambda \vec{a} \) becomes a unit vector. A unit vector has a magnitude of 1. ### Step-by-Step Solution: 1. **Understand the Magnitude of the Vector**: Given that \( \vec{a} \) is a non-zero vector with a magnitude \( |\vec{a}| = a \). 2. **Express the Magnitude of the Scaled Vector**: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

If vec a is a non zero vector a magnitude a' and lambda is a non a zero scalar,then lambdavec a is a unit vector if lambda=1 b.lambda=-1 c.a-| lambda| d.a=(1)/(| lambda|)

If (tan3A)/(tan A)=lambda then a possible value of (sin3A)/(sin A) is (A) (8)/(3) if lambda=3 (B) 1 if lambda=-1 (C) (1)/(5) if lambda=(-1)/(9) (D) 4 if lambda=2

If vec a,vec b,vec c are non-coplanar vectors and lambda is a real number then [lambda(vec a+vec b)quad lambda^(2)vec bquad lambdavec c]=[vec avec b+vec cquad vec b] then lambda=

If A satisfies the equation x^3-5x^2+4x+lambda=0 , then A^(-1) exists if lambda!=1 (b) lambda!=2 (c) lambda!=-1 (d) lambda!=0

If A,B and are collinear find lambda non-collinear such that vec c=(lambda-2)vec a+vec b and vec d=(2 lambda+1)vec a-vec b,vec c and vec d are collinear find lambda

If vec a,vec b,vec c are non-coplanar vectors and lambda is a real number then then vectors vec a+2vec b+3vec c,lambdavec b+4vec c and (2 lambda-1)vec c are non-coplanar for

If [vec a xxvec bvec d xxvec cvec c xxvec a] = lambda [vec with bvec c] ^ (2) then lambda is equal to

If a,b,c are non coplanner vectors and lambda is a real no.then the vector a +2b+3c,lambda b+4c and (2 lambda-1) c are non coplanner for:-