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For what values of lambda the vectors ba...

For what values of `lambda` the vectors `bar(i) - lambda bar(j) + 2bar(k), 8bar(i) + 6bar(j) - bar(k)` are at right angles.

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The correct Answer is:
`lamda=1`
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Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

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The number of distinct real values of lambda for which the vectors -lambda^(2)bar(i)+bar(j)+bar(k), bar(i)-lambda^(2)bar(j)+bar(k), bar(i)+bar(j)-lambda^(2)bar(k) are coplanar is

If the vectors 2bar(i) + lambda bar(j) - bar(k) and 4bar(i)-2bar(j)+2bar(k) are perpendicular to each other than find lambda .

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-PRODUCT OF VECTORS-SOLVED PROBLEMS
  1. For what values of lambda the vectors bar(i) - lambda bar(j) + 2bar(k)...

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  2. If veca=6veci+2vecj+3veck and vecb=2veci-9vecj+6veck then find veca.ve...

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

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  4. IF | veca + vecb|=| veca - vecb| , then what is the angle betwe...

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  5. If |veca|=11,|vecb|=23 and |veca-vecb|=30, then find the angle between...

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  6. If veca=veci-vecj-veck and vecb=2veci-3vecj+veck, then find the projec...

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  7. If P, Q, R and S are points whose position vectors are bari-bark, -bar...

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  8. If vectors lambda bar(i) - 3bar(j)+5bar(k), 2lambda bar(i) - lambdabar...

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  9. Let veca=2veci+3vecj+veck,vecb=4veci+vecj and vec(c)=veci-3vecj-7veck....

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  10. Show that the vectors 2hati-hatj+hatk,hati-3hatj-5hatkand3hati-4hatk f...

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  11. P.T the smaller angle theta between any two diagonals of a cube is giv...

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  12. Let bara,barb,barc be non-zero mutually orthogonal vectors. If xbara+y...

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  13. Let bara, barb and barc be mutually orthogonal vectors of equal magnit...

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

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

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

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

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

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

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

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

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