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Determine lambda, for which the volume o...

Determine `lambda`, for which the volume of the parallelopiped having coterminus edges `bar(i)+bar(j), 3bar(i) - bar(j) and 3bar(j) + lambdabar(k)` os 16 cubic units.

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The correct Answer is:
`+-4`
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Find the volume of the tetrahedron having the edges , bar(i) + bar(j) + bar(k), bar(i)-bar(j), bar(i) + 2bar(j) + bar(k) .

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Find the volume of the parallelopiped having co-tenninus edges are represented by the vectors 2 bar(i) - 3bar(j) + bar(k), bar(i) -bar(j) +2bar(k), 2bar(i) + bar(j) -bar(k) .

Compute 2 bar(j) xx (3bar(i) - 4bar(k)) + (bar(i)+2bar(j)) xx bar(k) .

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

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

Unit vectors along the diagonals of the parallelogram whose adjacent sides are bar(i)+bar(j)+bar(k) and bar(i)-bar(j)+bar(k) are

Find unit vector perpendicular to both bar(i) + bar(j) + bar(k) and 2bar(i) + bar(j) + 3bar(k) .

Find the vector equation of the plane passing through the points bar(i)-2bar(j)+5bar(k), -5bar(j)-bar(k), -3bar(i)+5bar(j) .

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

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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