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Find the Cartesian equation of the plane passing through the point `(-2,1,3)` and perpendicular to the vector `3bar(i) + bar(j) + 5bar(k)`.

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PRODUCT OF VECTORS-SOLVED PROBLEMS
  1. Let bara, barb and barc be mutually orthogonal vectors of equal magnit...

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  2. The vectors bar(AB) = 3bari - 2barj + 2bark and bar(BC) = -bari - 2bar...

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  3. Find the Cartesian equation of the plane passing through the point (-2...

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  4. Find the cartesian equation of the plane through the point A (2,-1,-4)...

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  5. Find the angle between the planes 2x-3y-6z=5 and 6x+2y-9z = 4.

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  6. Find unit vector orthogonal to the vector 3bari + 2barj + 6bark and co...

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  7. If veca=2veci-3vecj+5veck,vecb=-veci+4vecj+2veck, then find vecaxxvecb...

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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. Find the area of the parallelogram for which the vectors veca=2veci-3v...

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  10. If vec(a) xx vec(b) = vec(c ) xx vec(d) and vec(a) xx vec(c )= vec(b) ...

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

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  12. Let veca=2veci-j+veck and vecb=3i+4j-veck. If theta is the angle betwe...

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  13. Let vec(a), vec(b), vec(c ) be such that vec(c ) ne vec(0), vec(a) xx ...

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  14. Let veca = 2 hati+hatj-2hatk, vecb=hati+hatj. If vecc is a vector suc...

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

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  16. A non-zero vector bar(a), is parallel to the line of intersection of t...

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  17. If vec(a)= 4vec(i) + 5vec(j)- vec(k), vec(b)= vec(i)- 4vec(j) + 5vec(k...

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  18. For any vector bar(a) show that |bar(a) xx bar(i)|^(2) + |bar(a) xx ba...

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  19. If veca is non-zero vector and b,vec(c) are two vector such that vecax...

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  20. Prove that the vectors vec(a)=2veci-vecj+veck,vecb=veci-3vecj-5veck an...

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