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Write the value of hat(i).(hat(j)xxhat(...

Write the value of `hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+hat(k).(hat(i)xxhat(j))`.

A

0

B

`-1`

C

1

D

3

Text Solution

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The correct Answer is:
C
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Vector product of three vectors is given by vec(A)xx(vec(B)xxvec(C))=vec(B)(vec(A).vec(C))-vec(C)(vec(A).vec(B)) The value of hat(i)xx(hat(i)xxhat(j))+hat(j)xx(hat(j)xxhat(k))+hat(k)xx(hat(k)xxhat(i)) is

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Find the value of : (i) (hat(i) xxhat(j))*hat (k) + hat(i)* hat(j) (ii) (hat(k) xx hat(j))* hat(i) +hat(j)* hat(k) hat(i) xx (hat(j) + hat(k) )+hat(j) xx(hat(k) +hat(i))+ hat(k) xx (hat(i)+hat(j))

(hat(k)xx hat(j)).hat(i)+hat(j).hat(k)= ………….

If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j) , then the vectors (a*hat(i))hat(i)+(a*hat(j))hat(j)+(a*hat(k))hat(k), (b*hat(i))hat(i)+(b*hat(j))hat(j)+(b*hat(k))hat(k) and hat(i)+hat(j)-2hat(k)

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Find the angle between hat(i)+hat(j)+hat(k) and hat(i)+hat(j)-hat(k) .

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Express -hat(i)-3hat(j)+4hat(k) as the linear combination of the vectors 2hat(i)+hat(j)-4hat(k) , 2hat(i)-hat(j)+3hat(k) and 3hat(i)+hat(j)-2hat(k) .

MODERN PUBLICATION-VECTOR ALGEBRA -Objective Type Questions (A. Multiple Choice Questions)
  1. If (2hat(i)+6hat(j)+ 27hat(k))xx(hat(i)+phat(j)+qhat(k))=vec(0), then ...

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  2. If vec(a)=2hat(i)+3hat(j)-hat(k), then |vec(a)| is :

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  3. Write the value of hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+ha...

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  4. For mutually perpendicular unit vectors hat(i), hat(j), hat(k), we hav...

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  5. Direction - ratios of vector vec(a)=hat(i)+hat(j)-2hat(k) are :

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  6. If vec(a)=hat(i)+2hat(j), then |vec(a)| is :

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  7. Direction - cosines of vec(a)=hat(i)+hat(j)-2hat(k) are :

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  8. If p hat(i)+3hat(j) is a vector of magnitude 5, then the value of p is...

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  9. If is the angle between any two vectors vec a and vec b , t...

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  10. The inequality |vec(a).vec(b)|le |vec(a)||vec(b)| is called :

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  11. The vectors vec(a) and vec(b) are perpendicular if :

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  12. Find the angle between two vectors vec a and vec b with magnitudes 1 a...

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  13. Find | vec a- vec b|,\ if:| vec a|=2,\ | vec b|=3\ a n d\ vec adot ve...

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  14. The angle between the vectors : vec(a)=hat(i)+2hat(j)-3hat(k) and 3...

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  15. The D.C.'s of the vector hat(i)+2hat(j)+3hat(k) are :

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  16. If vec(a)=2hat(i)+2hat(j)+3hat(k), then its magnitude is :

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  17. If vec(a) and vec(b) are unlike vectors, then the angle between them i...

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  18. The angle between the vectors hat(i)-hat(j) and hat(j)+hat(k) is :

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  19. If vec(a).vec(b)=|vec(a)xx vec(b)|, then angle between vector vec(a) a...

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  20. Find the projection of the vector hat i+3 hat j+7 hat k on the vecto...

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