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If (3hati+4hatj+9hatk) and (a hati-3hatj...

If `(3hati+4hatj+9hatk)` and `(a hati-3hatj+1hatk)` are perpendicualr to each other then a = ………………

A

1

B

`-1`

C

7

D

`-7`

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If 4hati+5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+hatk) are position vectors of the points A, B, C and D then prove that A, B, C, D are coplannar.

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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. If bar(a)=(3,1,-2) and bar(b)=(1,3,-2) then (bar(a)" "^(hat)bar(b)) = ...

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  2. If bar(x)=(1,1,-1),bar(y)=(-1,2,2) and bar(z)=(-1,2,-1) then the unit ...

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  3. If (3hati+4hatj+9hatk) and (a hati-3hatj+1hatk) are perpendicualr to e...

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  4. If |bar(a)|=2,|bar(b)|=4,|bar( c )|=1 and bar(a)+bar(b)=-bar( c ) then...

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  5. If |bar(x)|=|bar(y)|=2 and (bar(x)" "^(hat)bar(y))=theta then |bar(x)-...

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  6. The projection of the vector (-4,-2,4) on (2,1,1) is ………….

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  7. The magnitude of the projection of vector (4, 1, 3) and (1, -2, 3) is ...

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  8. The unit vector perpendicular to (3,-4) in R^(2) is ………………

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  9. The unit vector perpendicualr to (3, 4)is ……………….

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  10. If |bar(x)|=|bar(y)|=1 and bar(x)|bar(y), then |bar(x)-bar(y)| =……………

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  11. bar(a)=(-3,1,0),bar(b)=(1,-1,-1) then |"Comp"(bar(b))bar(a)| = …………

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  12. If bar(a)+bar(b)+bar( c )=bar(0) and |bar(a)|=3,|bar(b)|=5,|bar( c )|=...

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  13. A(1, -2, 4), B(5, -1, 7), C(3, 6, -2) and D(4, 5, -1) are given vector...

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  14. In a right angled triangle ABC, hypotenuse AB=P then bar(AB).bar(AC)+b...

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  15. squareABCDEF is a regular hexagone with each side a. bar(AB).bar(AF)+(...

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  16. For vectors bar(a),bar(b),bar( c ),|bar(a)-bar( c )|=|bar(b)-bar( c )|...

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  17. A unit vector is coplanner with bar(i)+bar(j)+2bar(k) and bar(i)+2bar(...

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  18. The angle between the unit vectors bar(a) and bar(b) is theta. If bar(...

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  19. For unit vectors bar(a) and bar(b), if bar(a)+2bar(b) and 5bar(a)-4bar...

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  20. bar(a)=2bar(i)-3bar(j)+6bar(k) and bar(b)=-2bar(i)+2bar(j)-bar(k) then...

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