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Let overline(a)=hat(i)-hat(k), overline(...

Let `overline(a)=hat(i)-hat(k), overline(b)=xhat(i)+hat(j)+(1-x)hat(k), overline(c)=yhat(i)+xhat(j)+(1+x-y)hat(k)`. Then `[[overline(a), overline(b), overline(c)]]` depends on

A

only x

B

only y

C

neither x nor y

D

both x and y

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The correct Answer is:
C
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NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. If the vectors overline(a)=4hat(i)+11hat(j)+mhat(k), overline(b)=7hat...

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  2. If overline(a)=hat(i)-2hat(j)+hat(k), overline(b)=xhat(i)-5hat(j)+3hat...

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  3. Let overline(a)=hat(i)-hat(k), overline(b)=xhat(i)+hat(j)+(1-x)hat(k),...

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  4. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

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  5. If the vectors ahat(i)+hat(j)+hat(k), hat(i)+bhat(j)+hat(k), hat(i)+ha...

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

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

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

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

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

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

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

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

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

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

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

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

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

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