Home
Class 12
MATHS
In a trapezium ABCD the vector B vec C ...

In a trapezium ABCD the vector `B vec C = lambda vec(AD).` If `vec p = A vec C + vec(BD)` is coillinear with `vec(AD)` such that `vec p = mu vec (AD),` then

A

`mu=lamda+1`

B

`lamda=mu+1`

C

`lamda+mu=1`

D

`mu=2+lamda`

Text Solution

Verified by Experts

The correct Answer is:
A
We have, `p=AC+BD=AC+BC+CD`
`=AC+lamdaAD+CD`
`=lamdaAD+(AC+CD)=lamdaAD+AD=(lamda+1)AD`
Therefore, `p=muAD impliesmu=lamda+1`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 1|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 2|17 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|19 Videos

Similar Questions

Explore conceptually related problems

Let lambda = vec a xx (vec b + vec c), vec mu = vec b xx (vec c + vec a) and vec nu = vec c xx (vec a + vec b). Then

vec a,vec b,vec c are three non zero vectors no two of which are collonear and the vectors vec a+vec b be collinear with vec c,vec b+vec c to collinear with vec a then vec a+vec b+vec c the equal to ?(A)vec a (B) vec b(C)vec c (D) None of these

If vec a is a non-zero vector and vec a * vec b = vec a * vec c, vec a xxvec b = vec a xxvec c, then

A vector equation of the line of intersection of the planes vec r = vec b + lambda_ (1) (vec b-vec a) + mu_ (1) (vec a + vec c) vec r = vec c + lambda_ (2) (vec b-vec c) + mu_ (2) (vec a + vec b) and vec a, vec b, vec c being non coplanar vectors is

For any three vectors vec a, vec b, vec c, (vec a-vec b) * (vec b-vec c) xx (vec c-vec a) is equal to

If vec a,vec b and vec c be any three vectors then show that vec a+(vec b+vec c)=(vec a+vec b)+vec c

If the vectors vec a+vec b+vec c,vec a+lambdavec b+2vec c,-vec a+vec b+vec c are linearly dependent then lambda

Consider Delta ABC with A (case a), B (case b) and C (case c). If vec b * (vec a + vec c) = vec b * vec b + vec a * vec c | vec b-vec a | = 3; | vec c-vec b | = 4, then the angle between the median vec AM and vec AD is:

Non-zero vectors vec a, vec b and vec c satisfy vec a * vec b = 0, (vec b-vec a) (vec b + vec c) = 0 and 2 | vec b + vec c | = | vec b -vec a | If vec a = muvec b + 4vec c then possible value of mu are