Home
Class 12
MATHS
The vectors x hati + (x+1)hatj + (x+2)ha...

The vectors `x hati + (x+1)hatj + (x+2)hatk, (x+3)hati+ (x+4)hatj + (x+5)hatk `
and `(x+6)hati + (x+7)hatj+ (x+8)hatk` are coplanar if `x` is equal to.

A

1

B

`-3`

C

`4`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`xhati+(x+1)hatj+(x+2)hatk,(x+3)hati+(x+4)hatj+(x+5)hatk and (x+6)hati+(x+7)hatj+(x+8)hatk` are coplanar. We have
determinant of their coefficient as `|(x,x+1,x+2),(x+3,x+4,x+5),(x+6,x+7,x+8)|`
Applying `C_(2) to C_(2)-C_(1) and C_(3) to C_(3)-C_(1)`, we have
`|(x,1,2),(x+3,1,2),(x+6,1,2)|=0`, hence, `x in R`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Show that the vectors, vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hatk and vec( c )=hati-3hatj+5hatk are coplanar.

The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hatj) is ……..

If the vectors 4hati+11hatj+mhatk,7hati+2hatj+6hatk and hati+5hatj+4hatk are coplanar, then m is equal to

Show that the vectors vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hatk and vec( c )=hati-hatj+5hatk are coplannar.

hati*(hatkxx hatj)+hatj*(hati xx hatk)+hatk*(hatj xx hati)+hati*(hati xx hatj)+hatj*(hatj xx hatk) = ………..

Find lambda if the vectors hati-hatj+hatk, 3hati-hatj+2hatk and hati+lambda hatj-3hatk are coplannar.

hati*(hatj xx hatk)+hatj*(hati xx hatk)+hatk*(hati xx hatj) =……………

If the vectors hati-hatj+hatk,3hati+hatj+2hatk and hati+lambda hatj-3hatk are coplanar then find the value of lambda .

The value of lamda for which the four points 2hati+3hatj-hatk,hati+2hatj+3hatk,3hati+4hatj-2hatk and hati-lamdahatj+6hatk are coplanar.

Show that the vectors 2hati-3hatj+4hatk and -4hati+6hatj-8hatk are collinear.