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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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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.

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

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

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

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

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  5. Prove that bar(a)x[bar(a)x(bar(a) x bar(b))] = (bar(a).bar(a))(bar(b)x...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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