Show that (bar(a)+bar(b)) . [(bar(b)+bar...

Show that `(bar(a)+bar(b)) . [(bar(b)+bar(c)) xx (bar(c )+bar(a))] = 2[bar(a)bar(b)bar(c )]`.

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Compute bar(a) xx (bar(b) + bar(c )) + bar(b) xx (bar(c ) +bar(a)) + bar(c ) xx (bar(a)+bar(b))

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.

If bar(a), bar(b), bar(c ) respresents the vertices A, B, and C respectively of DeltaABC then prove that |(bar(a) xx bar(b)) + (bar(b) xx bar(c ))+ (bar(c ) xx bar(a))| is twice the area of DeltaABC .

bar(a) , bar(b), bar (c ) , are non-coplanar vectors, Prove that the following four points are coplanar. 6bar(a) + 2bar(b) - bar(c ), 2bar(a) - bar(b) + 3bar(c ), -bar(a) + 2bar(b)-4bar(c ), -12bar(a)-bar(b)-3bar(c ) .

Find the point of intersection of the line bar(r)=2bar(a)+bar(b)+t(bar(b)-bar(c)) and the plane bar(r)=bar(a)+x(bar(b)+bar(c))+y(bar(a)+2bar(b)-bar(c)) where bar(a), bar(b), bar(c) are non coplanar vectors.

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.

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.

SRISIRI PUBLICATION-IPE SCANNER (TEXUAL BITS)-Very Short Questions (2 marks) (Product of vectors )

If bar(a)=bar(i)-2bar(j)+bar(k), bar(b)=2bar(i)+bar(j)+bar(k), bar(c )...
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If bar(a),bar(b),bar(c ) are mutually perpendicular unit vectors, then...
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Show that (bar(a)+bar(b)) . [(bar(b)+bar(c)) xx (bar(c )+bar(a))] = 2[...
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Prove that bar(a)x[bar(a)x(bar(a) x bar(b))] = (bar(a).bar(a))(bar(b)x...
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Find the value of [bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-b...
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Ig |bar(a)| = 11 ,|bar(b)| = 23,|bar(a)-bar(b)| = 30 then find the ang...
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If bar(P),bar(Q),bar(R) and bar(S) are points whose position vectors a...
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Let bar(a) = 2bar(i) + 3bar(j) + bar(k), bar(b) = 4bar(i) + bar(j) and...
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Let bar(e1) and bar(e2) be unit vectors making angle theta. If 1/2|bar...
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Find the equation of the line passing through the point 2bar(i)+3bar(j...
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If bar(a)=2bar(i)-3bar(j)+5bar(k),bar(b)=-bar(i)+4bar(j)+2bar(k), then...
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If bar(a)bar(b)bar(c ) and bar(d) are vectors such that bar(a) xx bar(...
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If bar(a).bar(b) = bar(a).bar(c ) and bar(a) xx bar(b) = bar(a) xx bar...
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Find the equation of the plane passing through the point A=(2,3,-1),B=...
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Find the equation of the plane passing though the point A = (3, -2,-1)...
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Find the distance of a point (2,5,-3) form plane bar(r ).(6bar(i) - 3b...
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Find the angle between line (x+1)/2 = y/3 = (z-3)/6 and the plane 10x ...
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Compute [bar(i) - bar(j). bar(j) - bar(k). bar(k) -bar(i)].
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If bar(a) = bar(i) -2bar(j)-3bar(k),bar(b)=2bar(i)+bar(j)-bar(k),bar(c...
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For non coplanar vector, bar(a), bar(b) and bar(c ) determine p for wh...
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