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

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

Text Solution

AI Generated Solution

To show that \((\vec{a} - \vec{b}) \times (\vec{a} + \vec{b}) = 2 \vec{a} \times \vec{b}\), we can follow these steps: ### Step 1: Expand the left-hand side using the distributive property of the cross product. We start with the expression: \[ (\vec{a} - \vec{b}) \times (\vec{a} + \vec{b}) \] Using the distributive property, we can expand this as follows: ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.3|18 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercises|15 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercise 2.1|18 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 geometrical interpretation of it.

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

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

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

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

Prove that : veca*(vecb+vec c)xx(veca+2vecb+3vec c)=[veca vecb vec c]

Prove that veca*(vecb+vec c)xx (veca+3vecb+2vec c)=-(veca vecb vecc )

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

Prove that (veca+ vecb)*( veca+ vecb)=|veca|^2+| vecb|^2 , if and only if veca , vecb are perpendicular, given veca!= vec0, vecb!= vec0

If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ (vecb + veca) xx (2 veca + vecb)] = veca+vecb then angle theta " between " veca and vecb is