If `veca,vecb and vecc` are three non coplanar vectors and `vecr` is any vector in space, then `(vecxxvecb),(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(

Question

If `veca,vecb and vecc` are three non coplanar vectors and `vecr` is any vector in space, then `(vecxxvecb),(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(

If `veca,vecb and vecc` are three non coplanar vectors and `vecr` is any vector in space, then `(vecxxvecb),(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)=` (A) `[veca vecb vecc]` (B) `2[veca vecb vecc]vecr` (C) `3[veca vecb vecc]vecr` (D) `4[veca vecb vecc]vecr`
A. `[veca vecb vecc]vecr`
B. `2 [veca vecb vecc]vecr`
C. `3 [veca vecb vecc]vecr`
D. none of these

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - b
` (veca xx vecb) xx (vecr xx vecc)`
`= ((veca xx vecb) .vecc) vecr- ((veca xx vecb).vecr) .vecc`
` [veca vecb vecc] vecr- [veca vecb vecr] vecc`
similarly, ` (vecb xx vecc) xx (vecr xx veca)`
`= [vecb vecc veca] vecr - [vecb vecc vecr] veca`
` and (vecc xx veca) xx (vecr xx vecb) = [vecc veca vecb] vecr - [vecc veca vecr] vecb`
` Rightarrow (veca xx vecb ) xx (vecr xx vecc) + (vecb xx vecc)`
`x (vecr xx veca) + (vecc xx veca0 xx (vecr xx vecb)`
` 3[ veca vecb vecc] vecr - ([vecb vecc vecr]veca + [vecc veca vecr] vecr + [veca vecb vecr] vecc)`
` 3[veca vecb vecc] vecr - [veca vecb vecc] vecr = 2 [veca vecb vecc] vecr`