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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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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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OBJECTIVE RD SHARMA ENGLISH-ALGEBRA OF VECTORS-Exercise
  1. The vector vec c , directed along the internal bisector of the angle...

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  2. A, B have vectors vec a , vec b relative to the origin O and X, Y d...

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  3. If a vector ofmagnitude 50 is collinear with vector vecb = 6 hat i - 8...

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  4. The vector vec c , directed along the internal bisector of the angle...

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  5. Let vec a , vec b ,vec c are three non- coplanar vectors such that ...

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  6. If vec a, vec b , vec c are three non- coplanar vectors such that v...

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  7. veca, vecb ,vecc are three non zero vectors no two of which are collon...

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

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  9. The points with position vectors 60hati+3hatj,40hati-8hatj, ahati-52ha...

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  10. If the points with position vectors 10 hat i+3 hat j ,12 hat i-5 ha...

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  11. If C is the middle point of AB and P is any point outside AB, then

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  12. The median AD of the DeltaABC is bisected at E.BE meets AC in F. then,...

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  13. In a trapezium, the vector BC=lamdaAD. We will then find that p=AC+BD ...

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  14. If vec xa n d vec y are two non-collinear vectors and A B C isa trian...

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  15. If D, E, F are respectively the mid-points of AB, AC and BC respectiv...

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  16. Forces 3 O vec A , 5 O vec B act along OA and OB. If their resultant ...

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  17. If aBCDEF is a regular hexagon with A vec(B) = vec(a) and B vec(C ) =...

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  18. If A,B and C are the vertices of a triangle with position vectors vec(...

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  19. Let vec a=hati -2 hatj + 3 hatk, vec b = 3 hati + 3 hatj -hat k and v...

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  20. If G is the intersection of diagonals of a parallelogram A B C D and O...

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