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If veca, vecb and vecc are any three vec...

If `veca, vecb` and `vecc` are any three vectors forming a linearly independent system, then `AA theta in R`
`vecp=vecacostheta+vecbsintheta+vecc(cos2theta)`
`vecq=vecacos((2pi)/(3)+theta)+vecbsin((2pi)/(3)+theta) + vecc(cos 2)((2pi)/(3)+theta)`
and `vecr=vecacos(theta-(2pi)/(3))+vecbsin(theta-(2pi)/(3))+vecc cos2(theta-(2pi)/(3))`
then `[vecpvecqvecr]`

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ARIHANT MATHS ENGLISH-PRODUCT OF VECTORS-Exercise (Single Option Correct Type Questions)
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  2. . Let a, b > 0 and vecalpha=hati/a+4hatj/b+bhatk and beta=bhati+ahatj+...

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  3. If veca, vecb and vecc are any three vectors forming a linearly indepe...

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  4. Two adjacent sides of a parallelogram A B C D are given by vec A B=...

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  5. If in a triangleABC, BC=(e)/(|e|)-(f)/(|f|) and AC=(2e)/(|e|): |e|ne|f...

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  6. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  7. In triangle ABC the mid point of the sides AB, BC and AC respectively ...

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  8. The angle between the lines whose directionn cosines are given by 2l-m...

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  9. A line makes an angle theta both with x-axis and y-axis. A possible ra...

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  10. Let veca, vecb and vecc be the three vectors having magnitudes, 1,5 an...

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  11. Find the perpendicular distance of a corner of a cube of unit side len...

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  12. If p,q are two-collinear vectors such that (b-c)ptimesq+(c-a)p+(a-b)q...

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  13. Let a=hat(i)+hat(j)+hat(k), b=-hat(i)+hat(j)+hat(k), c=hat(i)-hat(j)+h...

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  14. A parallelepiped is formed by planes drawn parallel to coordinate axes...

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  15. Let a,b,c be three non-coplanar vectors and d be a non-zerro vector, w...

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  16. If alpha(axxb)+beta(bxxc)+gamma(cxxa)=0, then

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  17. Let area of faces triangleOAB=lambda1, triangleOAC=lambda2, triangleOB...

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  18. Given four non zero vectors bar a,bar b,bar c and bar d. The vectors ...

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  19. The shortest distance between a diagonal of a unit cube and the edge s...

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  20. 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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