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The scalar vecA.(vecB+vecC)xx(vecA+vecB+...

The scalar `vecA.(vecB+vecC)xx(vecA+vecB+vecC)` equals (A) 0 (B) `[vecA vecB vecC]+[vecB vecC vecA]` (C) `[vecA vecB vecC]` (D) none of these

A

0

B

`[vecA vecB vecC]+ [vecB vecC vecA] `

C

`[vecA vecB vecC]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
`vecA.(vecB + vecC) xx (vecA + vecB +vecC)`
` vecA . ([vecB xx vecA +vecB xx vecB + vecC + vecC xx vecA + vecC xx vecB +vecC xx vecC]`
`= vecA.vecBxxvecA + vecA.vecBxxvecC+vecA.vecCxx vecA + vecA+ vecC xx vecB " " ( "using" veca xx veca =0)`
`0+[vecA vecB vecC]+0+ [vecA vecC vecB]`
`[vecA vecB vecC]-[vecA vecB vecC]`
=0
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -JEE Previous Year (Single Question)
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  6. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

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  7. Let vecu,vecv and vecw be vectors such that vecu+ vecv + vecw =0 if |v...

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  8. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  9. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  11. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  12. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  13. Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(v...

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  14. If veca,vecb, vecc are unit coplanar vectors then the scalar triple pr...

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  16. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  17. Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a u...

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  18. The value of a so thast the volume of parallelpiped formed by vectors ...

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  19. If veca = (hati + hatj +hatk), veca. vecb= 1 and vecaxxvecb = hatj -ha...

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