Advertisement Remove all ads

Show that the vectors a,b are coplanar if a+b, b+c are coplanar. - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Show that the vectors `veca, vecb` are coplanar if `veca+vecb, vecb+vecc ` are coplanar.

Advertisement Remove all ads

Solution

It is given that `veca+vecb, vecb+vecc `

Therefore

Scalar triple product=Volume of the parallelopoid=0

`(veca+vecb).[(vecb+vecc)xx(vecc+veca)]=0`

`=>(veca+vecb).|__(vecbxxvecc)+(vecbxxveca)+0+(veccxxveca)__|=0`

`=>veca.(vecbxxvecc)+veca.(vecbxxveca)+veca.(veccxxveca)+vecb.(vecbxxvecc)+vecb.(veccxxveca)=0`

⇒ [abc]+0+0+0+0+[bca]=0

2[abc]=0

[abc]=0

Therefore, the vectors `veca,vecb `are coplanar.

Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors
  Is there an error in this question or solution?
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×