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Prove that the four points 4bari + 5ba...

Prove that the four points ` 4bari + 5barj +bark, - (barj + bark) , 3bari + 9barj + 4bark , - 4bari + 4barj +4bark` are coplanar.

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Find the value of lamda for which the four points with position vectors bari - 2barj + bark, 2bari - barj + lamdabark , 2bari + barj -bark and 3bari + barj - bark are coplanar.

Prove that the vectors bara= 2bari - barj + bark, barb = bari -3barj -5bark and barc=3bari -4barj -4bark are coplanar.

Show that the vectors bara= bari + 3barj + bark, barb =2bari - barj-bark and barc=7barj +3bark are coplanar.

Find the volume of tetrahedron formed by the four planes barr. (bari + barj) = 0 , barr. (barj + bark) = 0, barr. (bari + bark) = 0 and barr. (bari + barj + bark) = 4.

If the three vectors 2bari -barj +bark, bari+ 2barj -3bark, 3bari + lamdabarj + 5bark are coplanar then lamda =

The four points whose position vectors are 6bari -7 barj, 16bari -29barj-4bark, 3barj-6bark, 2bari +5barj +10bark are

[bari-barj bark]+[-bari-barj bark]+[bari-bark bark] =

If bara = bari - 2barj - 3bark , barb= 2bari + barj - bark , barc = bari + 3barj - 2bark find bara xx (barb xx barc) .

AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-EXERCISE - 4.1 (SHORT ANSWER QUESTIONS)
  1. Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2ba...

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  2. For non - coplanar vectors bara,barb and barc determine p for which th...

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  3. If bara,barb,barc are non-coplanar vectors, prove that points with pos...

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  4. Show that the four points -bara+ 4barb - 3barc, 3bara +2barb-5barc,-3b...

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  5. Prove that the four points 4bari + 5barj +bark, - (barj + bark) , 3b...

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  6. Find lambda in order that the four points A(3,2,1), B(4, lambda,5),C(4...

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  7. If bar(a),bar(b),bar(c ) are mutually perpendicular unit vectors, then...

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  8. Let bara be perpendicular to both barb,barc. If |bara|=2, |barb|=3, |b...

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  9. Let bara=bari-bark, barb=xbari + barj+(1-x)bark and c-ybari+xbarj+(1+x...

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  10. If bara=(1,-1,-6),barb=(1,-3,4) and barc(-2,-5,3) then compute baraxx(...

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  11. i) Show that barixx(baraxxbari)+barjxx(baraxxbarj)+barkxx(baraxxbark...

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  12. Show that 3 vectors baraxx(barb xxbarc),barb xx(barcxxbara), barc xx (...

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  13. If barabarbbarc are three unit vectors such that baraxx(barbxxbarc)=1/...

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  14. If bara,barb and barc are non zero non-collinear vectors and theta(ne0...

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  15. Show that i) baraxx(baraxx(baraxxbarb))=(bara.bara)(barbxxbara) ii...

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  16. If the four vectors a,b,c,d are coplanar, then (a xx b) xx (c xx d) =

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  17. Prove that [barbxxbarc barcxxbara baraxxbarb]=[bara barb barc]^(2...

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  18. If (barbxxbarc)xx(barcxxbara)=3barc, then find [barbxxbarc barcxxbar...

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  19. If bara=2bari+barj-bark,barb=-bari+2barj-4bark,barc=bari+barj+bark the...

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  20. If bara,barb,barc,bard are four vectors, then show that (baraxxbarb).(...

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