Home
Class 12
MATHS
The vector(s) which is /are coplanar wit...

The vector(s) which is /are coplanar with vectors `hati +hatj + 2hatk and hati + 2hatj +hatk` and perpendicular to vector `hati + hatj +hatk` , is /are

A

`hatj - hatk`

B

`-hati + hatj`

C

`hati -hatj`

D

`-hatj +hatk`

Text Solution

Verified by Experts

The correct Answer is:
a,d
Any vector in the plane of `veca = hati +hatj + 2hatk and vecb = hati + 2hatj + hatk` is
`vecr=lamda(hati+hatj+2hatk) +mu(hati+2hatj+hatk)`
`= (lamda+mu)hati+(lamda+2mu)hatj= (2lamda+mu)hatk`
Also `vecr` is perpendicular to the vector `hati + hatj +hatk`
`Rightarrow vecr.vecc=0`
` Rightarrow lamda + mu =0`
Possible vectors are `hatj -hatk or -hatj +hatk`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise single correct answer type|28 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

Similar Questions

Explore conceptually related problems

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

The vectors which is/are coplanar with vectors hati+hatj+2hatk and hati+2hatj+hatk and perpendicular to the vector hati+hatj+hatk is /are (A) hatj-hatk (B) -hati+hatj (C) hati-hatj (D) -hatj+hatk

A vector coplanar with vectors hati + hatj and hat j + hatk and parallel to the vector 2hati -2 hatj - 4 hatk , is

A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2hatk and vecb = hati + hatj + hatk, and perpendicular to the vector vecc = hati + hatj +hatk is

Prove that the vectors A=2hati-3hatj+hatk and B=hati+hatj + hatk are mutually perpendicular .

A vector P=3hati-2hatj+ahatk is perpendicular to the vector Q=2hati+hatj -hatk, The value of a is

The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is (a) (2hati - 6hatj + hatk)/sqrt41 (b) (2hati-3hatj)/sqrt13 (c) (3 hatj -hatk)/sqrt10 (d) (4hati + 3hatj - 3hatk)/sqrt34

Unit vector perpnicular to vector A=-3hati-2hatj -3hatk and 2hati + 4hatj +6hatk is

The unit vector perpendicular to the vectors 6hati+2hatj+3hatk and 3hati-6hatj-2hatk , is

The vector vecB=5hati+2hatj-Shatk is perpendicular to the vector vecA=3hati+hatj+2hatk if S=