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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

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

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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 -Miscellaneous Exercise on Chapter 10
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  2. Find the scalar components and magnitude of the vector joining the po...

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  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

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  4. If vec(a)=vec(b)+vec(c ), then is it true that |vec(a)|=|vec(b)|+|vec(...

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  5. Find the value of x for which x( hat i+ hat j+ hat k)is a unit vector...

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  6. Find a vector of magnitude 5 units, and parallel to the resultant of ...

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  7. If -> a= hat i+ hat j+ hat k , -> b=2 hat i- hat j+3 hat k and -...

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  8. Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are col...

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  9. Find the position vector of a point R which divides the line joinin...

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  10. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

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  11. Show that the direction cosines of a vector equally inclined to the a...

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  12. Let -> a= hat i+4 hat j+2 hat k , -> b=3 hat i-2 hat j+7 hat k and...

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  13. The scalar product of the vector hat i+ hat j+ hat kwith a unit vect...

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  14. If vec a , vec b , vec c are mutually perpenedicular vectors of eq...

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  15. Prove that ( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2 , if and o...

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

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  17. If vec a\ a n d\ vec b be two unit vectors and theta is the angle be...

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

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  19. If is the angle between any two vectors -> a and -> b , then ...

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