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Let alpha,beta and gamma be distinct rea...

Let `alpha,beta and gamma` be distinct real numbers. The points with position vectors

A

are collinear

B

form an equilateral triangle

C

form a scalene triangle

D

form a right angled triangle

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The correct Answer is:
B
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Let alpha, beta, gamma be distinct real numbers. The points with position vectors alpha hati + beta hatj +gamma hat k , beta hati + gamma hatj +alpha hat k , gamma hati +alpha hatj + beta hatk

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If vec x , vec y are two non-zero and non-collinear vectors satisfying [(a-2)alpha^2+(b-3)alpha+c] vec x+[(a-2)beta^2+(b-3)beta+c] vec y+[(a-2)gamma^2+(b-3)gamma+c]( vec xxx vec y)=0,w h e r ealpha,beta,gamma are three distinct real numbers, then find the value of (a^2+b^2+c^2-4)dot

If a,b,c are distinct positive real numbers, then

Let alpha,beta,gamma and delta are four positive real numbers such that their product is unity, then the least value of (1+alpha)(1+beta)(1+gamma)(1+delta) is :

If alpha,beta "and" gamma are real number without expanding at any stage prove that |{:(1,cos(beta-alpha),cos(gamma-alpha)),(cos(alpha-beta),1,cos(gamma-beta)),(cos(alpha-gamma),cos(beta-gamma),1):}| =0.

Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat k ,cos(alpha-beta) hat i+ hat j+"cos"(gamma-beta) hat k and cos(alpha-gamma) hat i+cos(beta-gamma) hat k+a hat k where alpha,beta , and gamma are different angles. If these vectors are coplanar, show that a is independent of alpha,beta and gamma

If |(alpha^(2n),alpha^(2n+2),alpha^(2n+4)),(beta^(2n),beta^(2n+2),beta^(2n+4)),(gamma^(2n),gamma^(2n+2),gamma^(2n+4))|=((1)/(beta^(2))-(1)/(alpha^(2)))((1)/(gamma^(2))-(1)/(beta^(2)))((1)/(alpha^(2))-(1)/(gamma^(2))) {where alpha^(2), beta^(2) and gamma^(2) are al distinct}, then the value of n is equal to

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VMC MODULES ENGLISH-VECTORS -LEVEL -1
  1. If S is the cirucmcentre, G the centroid, O the orthocentre of a trian...

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  2. If veca, vecb, vecc are three non-zero vectors such that veca + vecb +...

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  3. Let alpha,beta and gamma be distinct real numbers. The points with pos...

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  4. If |veca|=4, |vecb|=4 and |vecc|=5 such that veca bot vecb + vecc, vec...

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  5. If vecu=veca-vecb, vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvec...

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  6. If the vectors vecc, \ veca=xhati+yhatj+zhatk and vecb=hatj are such ...

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  7. Given any vector, vecr,|vecr xx hati|^(2) + |vecr xx hatj|^(2) + |vecr...

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  8. The value of x fot which the angle between the vectors a=-3hat(i)+xhat...

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  9. If a,b and c are non-coplanar vectors and lamda is a real number, then...

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  10. Let vecb and vecc be non-collinear vectors. If veca is a vector such t...

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  11. Let O be the centre of a regular pentagon ABCDE and vec(OA) = veca, th...

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  12. If vecr=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca) and [veca vecb v...

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  13. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

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  14. Let veca=veci-veck,vecb=xveci+vecj+(1-x)veck and vecc=yveci+xvecj+(1+x...

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  15. Let veca, vecb and vecc be three units vectors such that 3veca + 4vecb...

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  16. The value of x for which the angle between veca=2x^(2)hati+4xhatj + ha...

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  17. Given three vectors veca=6hati-3hatj,vecb=2hati-6hatj and vecc=-2hati+...

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  18. If vecalpha+ vecbeta+ vecgamma=a vecdeltaa n d vecbeta+ vecgamma+ vec...

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  19. If unit vector vecc makes an angle pi/3 with hati + hatj, then minimum...

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  20. If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecb xx vecc...

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