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If [bara+2bar b 2bar b+bar c 5bar c+bar...

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

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bar a, bar b, bar c are three vectros, then prove that: (bar a xx bar b) xx bar c = (bar a. bar c) bar b-(bar b. bar c) bar a.

Let bar a = 2 bari + 4 bar j - 5 bark, bar b= bar i + bar j + bar k and bar c = bar j + 2 bar k . Find the unit vector in the opposite direction of bar a + bar b + bar c .

If bar a = 2 bar I + bar j - bar k, bar b = - bari + 2 bar j - 4 bar k and bar c = bar I + bar j + bar k , then find ( bar a xx bar b) cdot (bar b xx bar c) .

If bara,barb,barc are non-coplaner, then show that the vectors bara -bar b , barb + barc ,bar c + bara are coplanar

If bar(a) = 2bar(i) + 3bar(j) + 4bar(k), bar(b) = bar(i) + bar(j) -bar(k), bar(c ) = bar(i) - bar(j) + bar(k) , compute bar(a)x(bar(b)xbar(c )) and verify that it is perpendicular to bar(a) .

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)| .

If bar(a) = 2bar(i) - 3bar(j) + 5bar(k), bar(b) = -bar(i) + 4bar(j) + 2bar(k) then find bar(a) xx bar(b) and unit vector perpendicular to both bar(a), bar(b) [-26bar(i) - 9bar(j) + 5bar(k), +- 1/(sqrt(782))26bar(i)+9bar(j)-5bar(k)) .

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) " & " bar(a)- bar(b) .

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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