If bar(a),bar(b),bar(c ) are mutually pe...

If `bar(a),bar(b),bar(c )` are mutually perpendicular unit vectors, then find `[bar(a)bar(b)bar(c )]^(2)`.

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If bar(a), bar(b), bar(c) are linearly independent vectors, then show that bar(a)-3bar(b)+2bar(c), 2bar(a)-4bar(b)-bar(c), 3bar(a)+2bar(b)-bar(c) are linearly independent.

i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vectors. If bar(a)+bar(b) is collinear with bar(c) and bar(b)+bar(c) is collinear with bar(a) then find the vector bar(a)+bar(b)+bar(c) . ii) If bar(a)+bar(b)+bar(c)=alphabar(d), bar(b)+bar(c)+bar(d)=betabar(a) and bar(a), bar(b), bar(c) are non coplanar vectors, then show that bar(a)+bar(b)+bar(c)+bar(d)=bar(0) .

i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.

If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), bar(a)-3bar(b)+5bar(c) are

If bar(a)=2bar(i)-3bar(j)+5bar(k),bar(b)=-bar(i)+4bar(j)+2bar(k) , then find (bar(a)+bar(b))xx(bar(a)-bar(b)) and unit vector perpendicular to both bar(a)+bar(b)andbar(a)-bar(b)

If bar(a), bar(b), bar(c) are non coplanar, show that the vectors bar(a)+2bar(b)-bar(c), 2bar(a)-3bar(b)+2bar(c), 4bar(a)+bar(b)+3bar(c) are linearly independent.

bar(a), bar(b) , bar(c ) are pair wise non zero and non collinear vectors. If bar(a) + bar(b) is collinear with bar(c ) and bar(b) + bar(c ) is collinear with bar(a) then find vector bar(a) + bar(b) + bar(c ) .

If bar(a)bar(b)bar(c ) and bar(d) are vectors such that bar(a) xx bar(b) = bar(c ) xx bar(d) and bar(a) xx bar(c ) = bar(b)xxbar(d) . Then show that the vectors bar(a) - bar(d) and bar(b) -bar(c ) are parallel.

AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-EXERCISE - 4.1 (SHORT ANSWER QUESTIONS)

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2ba...
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For non - coplanar vectors bara,barb and barc determine p for which th...
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If bara,barb,barc are non-coplanar vectors, prove that points with pos...
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Show that the four points -bara+ 4barb - 3barc, 3bara +2barb-5barc,-3b...
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Prove that the four points 4bari + 5barj +bark, - (barj + bark) , 3b...
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Find lambda in order that the four points A(3,2,1), B(4, lambda,5),C(4...
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If bar(a),bar(b),bar(c ) are mutually perpendicular unit vectors, then...
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Let bara be perpendicular to both barb,barc. If |bara|=2, |barb|=3, |b...
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Let bara=bari-bark, barb=xbari + barj+(1-x)bark and c-ybari+xbarj+(1+x...
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If bara=(1,-1,-6),barb=(1,-3,4) and barc(-2,-5,3) then compute baraxx(...
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i) Show that barixx(baraxxbari)+barjxx(baraxxbarj)+barkxx(baraxxbark...
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Show that 3 vectors baraxx(barb xxbarc),barb xx(barcxxbara), barc xx (...
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If barabarbbarc are three unit vectors such that baraxx(barbxxbarc)=1/...
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If bara,barb and barc are non zero non-collinear vectors and theta(ne0...
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Show that i) baraxx(baraxx(baraxxbarb))=(bara.bara)(barbxxbara) ii...
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If the four vectors a,b,c,d are coplanar, then (a xx b) xx (c xx d) =
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Prove that [barbxxbarc barcxxbara baraxxbarb]=[bara barb barc]^(2...
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If (barbxxbarc)xx(barcxxbara)=3barc, then find [barbxxbarc barcxxbar...
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If bara=2bari+barj-bark,barb=-bari+2barj-4bark,barc=bari+barj+bark the...
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If bara,barb,barc,bard are four vectors, then show that (baraxxbarb).(...
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