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The value of hati.(hatj xx hatk)+hatj.(h...

The value of `hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hatj)` is ……..

A

0

B

`-1`

C

1

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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The value of hati.(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) is

hati*(hatkxx hatj)+hatj*(hati xx hatk)+hatk*(hatj xx hati)+hati*(hati xx hatj)+hatj*(hatj xx hatk) = ………..

Check whether the given three vectors are coplnar or non- coplanar : -2hati -2 hatj + 4hatk, -2hati + 4hatj -2hatk, 4hati - 2hatj - 2hatk .

The position vectors of the points A, B, C are 2 hati + hatj - hatk , 3 hati - 2 hatj + hatk and hati + 4hatj - 3 hatk respectively . These points

Find the direction cosines of the resultant of the vectors (hati+hatj+hatk),(-hati+hatj+hatk),(hati-hatj+hatk) and (hati+hatj-hatk) .

If veca = 2 hati - hatj + hatk , vecb = hati + hatj - 2 hatk, vecc= hati + 3 hatj- hatk, if veca is perpendicular to lamda vecb + vecc. then the value of lamda is ________.

The magnitude of the projection of hati+3hatj+7hatk on 7hati-hatj+8hatk is ……………..

If vec(u)=hati xx(vec(a)xx hati)+hatj xx(vec(a)xx hatj)+hatk xx(vec(a)xx hatk) then vec(u) = ………..

If the figure formed by the four points hati+hatj-hatk,2hati+3hatj,3hati+5hatj-2hatk and hatk-hatj is

Find the area of the triangle formed by the tips of the vectors vec(a) = hati - hatj - 3hatk, vec(b) = 4hati - 3hatj +hatk and vec(c) = 3 hati - hatj +2 hatk .

KUMAR PRAKASHAN-VECTOR ALGEBRA -MISCELLANEOUS EXERCISE - 10
  1. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

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  2. Find the scalar components and magnitude of the vector joining the poi...

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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 veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

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  5. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

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

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  7. If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk, ...

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

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

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  10. The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and ha...

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

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  12. Let vec(a)=hati+4hatj+2hatk,vec(b)=3hati-2hatj+7hatk and vec( c )=2hat...

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  13. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  14. If vec(a),vec(b),vec( c ) are mutually perpendicular vectors of equal ...

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  15. prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2), ...

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  16. If theta is angle between two vectors vec(a) and vec(b) then vec(a).ve...

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

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  18. The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hat...

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  19. If theta is the angle between any two vectors vecaandvecb, then |veca*...

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