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If bar(a).bar(b) = bar(a).bar(c ) and ba...

If `bar(a).bar(b) = bar(a).bar(c )` and `bar(a) xx bar(b) = bar(a) xx bar(c ), bar(a) != 0`, then show that `bar(b) = bar(c )`.

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Let bar(a),bar(b) be two non-collinear unit vectors, if bar(alpha) = bar(a) -(bar(a).bar(b))bar(b) and bar(beta) = bar(a) xx bar(b), then show that |bar(beta)| = |bar(alpha)| .

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)=bar(0) then prove that bar(a)xxbar(b)=bar(b)xxbar(c)=bar(c)xxbar(a) .

Let bar(a), bar(b), bar(c ) be unit vectors, suppose that bar(a). bar(b) = bar(a). bar(c )= 0 and the angle between bar(b) and bar(c ) is pi//6 then show that bar(a)= +-2 (bar(b) xx bar( c))

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) .

If bar(a) = 2bar(i) - 3bar(j) + bar(k) and bar(b) = bar(i) + 4bar(j) -2bar(k) , then find (bar(a) + bar(b))xx(bar(a)-bar(b))

If bar(a) = 2bar(i) - bar(j) + bar(k), and bar(b) = bar(i) - 3bar(j) - 5bar(k) then find |bar(a) xx bar(b)| .

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

SRISIRI PUBLICATION-IPE SCANNER (TEXUAL BITS)-Very Short Questions (2 marks) (Product of vectors )
  1. Prove that bar(a)x[bar(a)x(bar(a) x bar(b))] = (bar(a).bar(a))(bar(b)x...

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  2. Find the value of [bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-b...

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  3. Ig |bar(a)| = 11 ,|bar(b)| = 23,|bar(a)-bar(b)| = 30 then find the ang...

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  4. If bar(P),bar(Q),bar(R) and bar(S) are points whose position vectors a...

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  5. Let bar(a) = 2bar(i) + 3bar(j) + bar(k), bar(b) = 4bar(i) + bar(j) and...

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  6. Let bar(e1) and bar(e2) be unit vectors making angle theta. If 1/2|bar...

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  7. Find the equation of the line passing through the point 2bar(i)+3bar(j...

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  8. If bar(a)=2bar(i)-3bar(j)+5bar(k),bar(b)=-bar(i)+4bar(j)+2bar(k), then...

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  9. If bar(a)bar(b)bar(c ) and bar(d) are vectors such that bar(a) xx bar(...

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  10. If bar(a).bar(b) = bar(a).bar(c ) and bar(a) xx bar(b) = bar(a) xx bar...

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  11. Find the equation of the plane passing through the point A=(2,3,-1),B=...

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  12. Find the equation of the plane passing though the point A = (3, -2,-1)...

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  13. Find the distance of a point (2,5,-3) form plane bar(r ).(6bar(i) - 3b...

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  14. Find the angle between line (x+1)/2 = y/3 = (z-3)/6 and the plane 10x ...

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  15. Compute [bar(i) - bar(j). bar(j) - bar(k). bar(k) -bar(i)].

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  16. If bar(a) = bar(i) -2bar(j)-3bar(k),bar(b)=2bar(i)+bar(j)-bar(k),bar(c...

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  17. For non coplanar vector, bar(a), bar(b) and bar(c ) determine p for wh...

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  18. Determine lambda, for which the volume of the parallelopiped having co...

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  19. If [bara+2bar b 2bar b+bar c 5bar c+bara]=k[bar a bar b bar c]

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  20. Let bar(a),bar(b) be two non-collinear unit vectors, if bar(alpha) = b...

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