Home
Class 12
MATHS
Show that (veca-vecb)xx(veca+vecb)=2(vec...

Show that `(veca-vecb)xx(veca+vecb)=2(vecaxxvecb)`

Text Solution

Verified by Experts

`(veca-vecb)xx(veca+vecb)=(veca-vecb) xxveca+(veca-vecb)xxvecb` [ By distributivity of vector product over addition]
`= vecaxxveca-vecbexxveca+vecaxxvecb-vecbxxvecb` [ Again , by distributivity of vector product over addition ]
`=vec0 +vecaxxvecb+vecaxxvecb-vec0`
`= 2vecaxxvecb`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.1|18 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.2|15 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

Show that (veca-vecb)xx(veca+vecb)=2vecaxx vecb and give a genometrical interpretation of it.

Show that (veca-vecb)xx(veca+vecb)=2vecaxx vecb and give a geometrical interpretation of it.

Prove that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) also interpret this result.

Prove that: (2veca-vecb)xx (veca+2vecb)=5vecaxxvecb .

Prove that (veca+3vecb)xx(veca+vecb)+(3veca-5vecb)xx(veca-vecb)=0

Show that: (veca-vecd)xx(vecb-vecc)+(vecb-vecd)xx(vecc-veca)+(vecc-vecd)xx(veca-vecb) is independent of vecd .

Prove that: |(veca+vecb)xx(veca-vecb)|=2ab if veca_|_vecb

Show that: (veca+vecb).{(vecb+vecc)xx(vecc+veca)|=2{veca.(vecbxxvecc)}

If veca, vecb, vecc are vectors such that |vecb|=|vecc| then {(veca+vecb)xx(veca+vecc)}xx(vecbxxvecc).(vecb+vecc)=

If the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0