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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The correct Answer is:

`=2[bara barb barc]`

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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-PRODUCT OF VECTORS-2 D (VSAQ, SAQ,LAQ)

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