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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 -Exercise
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  2. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  3. The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA v...

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  4. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vecc|=|veca||vecb...

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  5. The volume of he parallelepiped whose sides are given by vec O A=2...

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  6. If veca , vecb , vecc are three non-coplanar vector and vecp...

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  7. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  8. If veca, vecb, vecc are three non - coplanar vector such that vecaxx(v...

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  9. Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0. If |v...

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

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  11. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  12. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  13. Let vec a=2i+j+k , vec b=i+2j-k and a unit vector vec c be coplanar....

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

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  15. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  16. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

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  17. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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

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  19. Let vec V=2 hat i+ hat j- hat ka n d vec W= hat i+3 hat kdot If vec ...

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  20. Find the value of a so that the volume of the parallelepiped formed...

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