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If overline(a)=hat(i)+hat(j), overline(b...

If `overline(a)=hat(i)+hat(j), overline(b)=hat(j)+hat(k), overline(c)=alphaoverline(a)+betaoverline(b)` and the vectors `hat(i)-2hat(j)+hat(k), 3hat(i)+2hat(j)-hat(k), overline(c)` are coplanar, then `(alpha)/(beta)=`

A

`0`

B

`-2`

C

`-3`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
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NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

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  2. If veca=hati+hatj+hatk, vecb=4hati+3hatj+4hatk and vecc=hati+alphahati...

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  3. If overline(a)=hat(i)+hat(j), overline(b)=hat(j)+hat(k), overline(c)=a...

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  4. Let a,b,c be distinct non- negative numbers . If the vectors ah...

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  5. Given vectors overline(a)=3hat(i)-6hat(j)-hat(k), overline(b)=hat(i)+4...

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  6. If the points A(2, 1, -1), B(0, -1, 0), C(lambda, 0, 4), D(2, 0, 1) ar...

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  7. If the points P(1, -1, -1), Q(3, 1, lambda), R(0, 2, 1), S(-2, 0, 1) a...

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  8. If the points A(-6, 3, 2), B(3, -2, 4), C(5, 7, 3), D(-13, lambda, -1)...

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  9. If the points A(3, 9, 4), B(0, -1, -1), C(lambda, 4, 4), D(4, 5, 1) ar...

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  10. If the points A(4, 5, 1), B(5, 3, 4), C(4, 1, 6), D(3, lambda, 3) are ...

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  11. If the points A(2, -1, 0), B(-3, lambda, 4), C(-1, -1, 4), D(0, -5, 2...

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  12. If the points A(2, -1, 1), B(4, 0, p), C(1, 1, 1), D(2, 4, 3) are copl...

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  13. If the origin and the points P(2, 3, 4), Q(1, 2, 3) and R(x,y, z) are ...

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  14. If the origin and the points A(1, 2, -2), B(1, -2, 3), C(x, y, z) are ...

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  15. If O(0, 0, 0), A(x, 1, -1), B(0, y, 2) and C(2, 3, z) are coplanar, th...

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  16. The position vectors of the point A, B , C and D are 3hat(i)-2hat(j)-h...

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  17. If the points A(2, -1, 0), B(-3, lambda, 4), C(-1, -1, 4), D(0, -5, 2)...

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  18. If the points A(1, -1, 1), B(-1, 1, 1), C(lambda, 1, 1), D(2, -3, 4) a...

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  19. If |[a, b, c], [a^(2), b^(2), c^(2)], [a^(3)+1, b^(3)+1, c^(2)+1]|=0 a...

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  20. If veca, vecb,vecc are non-coplanar vectors and lambda is a real numbe...

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