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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:
D
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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

hat(i)*(hat(j)timeshat(k))+hat(j)*(hat(k)timeshat(i))+hat(k)*(hat(i)timeshat(j))=

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)

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

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

Write the value of hat ixx( hat j+ hat k)+ hat jxx( hat k+ hat i)+ hat kxx( hat i+ hat j)dot

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 theta is the angle between two vectors vec a\ a n d\ vec b ,\ t ...

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  2. Let vec(a) and vec(b) be two unit vectors and theta is the angle betwe...

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

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  5. The area of the triangle whose adjacent sides are : vec(a)=3hat(i)+hat...

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  6. The magnitude of the vector 6hat(i)+2hat(j)+3hat(k) is :

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  7. The vector with initial point P(2,-3,5) and terminal point Q(3,-4,7) i...

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  8. The angle between the vectors hat i -hat j and hat j - hat k is

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  9. The value of 'lambda' for which the two vectors : 2hat(i)-hat(j)+2hat(...

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  10. If (2hat(i)+6hat(j)+ 27hat(k))xx(hat(i)+phat(j)+qhat(k))=vec(0), then ...

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

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

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

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

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

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

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

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

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

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

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