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Statement 1: If a(1)hati + a(2)hatj + a(...

Statement 1: If `a_(1)hati + a_(2)hatj + a_(3)hatk, vecbhati+b_(2)hatj + b_(3) hatk and c_(1)hati + c_(2)hatj + c_(3)hatk` are three mutually perpendicular unit vectors then `a_(1)hati + b_(1)hatj + c_(1)hatk,a_(2)hati +b_(2)hatj+c_(2) hatk and a_(3)hati + b_(3) hatj + c_(3) hatk` may be mutually perpendicular unit vectors.
Statement 2 : value of determinant and its transpose are the same.

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Statement 1: If a_(1)hati + a_(2)hatj + a_(3)hatk, vecb_(1)hati+b_(2)hatj + b_(3) hatk and c_(1)hati + c_(2)hatj + c_(3)hatk are three mutually perpendicular unit vectors then a_(1)hati + b_(1)hatj + c_(1)hatk,a_(2)hati +b_(2)hatj+c_(2) hatk and a_(3)hati + b_(3) hatj + c_(3) hatk may be mutually perpendicular unit vectors. Statement 2 : value of determinant and its transpose are the same.

prove that the vectors A=2hati-3hatj+hatk and B=hati+hatj + hatk are mutually perpendicular .

Let veca=a_1hati+a_2hatj+a_3hatk, vecb=b_1hati+b_2hatj+b_3hatk and vecc=c_1hati+c_2hatj+c_3hatk then show that vecaxx(vecb+vecc)=vecaxxb+vecaxxvecc

Show that the vectors 1/7(2hati+3hatj+6hatk), 1/7 (3hati-6hatj+2hatk) and 1/7 (6hati+2hatj-3hatk) are mutually perpendicular.

a_(1) hati+a_(2)hatj is a unit vector perpendicular to 4hati - 3 hatj if -

Fina a unit vector in the direaction of the resultant of the vectors hati - hatj + 3hatk, 2 hati + hatj- 2 hatk and hati + 2 hatj- 2 hatk.

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2 hati - hatj - hatk and vec(c) = hati +3 hatj - 2hatk find (vec(a) xx vec(b)) xx vec(c)

MOTION-VECTOR -EXERCISE - 4 ( LEVEL-II)
  1. Statement 1: If a(1)hati + a(2)hatj + a(3)hatk, vecbhati+b(2)hatj + b(...

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  2. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  3. Let the vectors veca, vecb,vecc and vecd be such that (vecaxxvecb)xx(v...

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  4. If veca, vecb and vecc are unit coplanar vectors, then the scalar trip...

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  5. If veca =hati + hatj-hatk, vecb = - hati = - hati + 2hatj + 2hatk and ...

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  6. Given that vectors veca and vecb asre perpendicular to each other, fin...

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  7. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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  8. The diagonals of a parallelogram are given by vectors 2hati+3hatj-6hat...

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  9. Find the all the values of lamda such that (x,y,z)!=(0,0,0)and x(hati+...

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  10. Two vertices of a triangle are at -hati+3hatj and 2hati+5hatj and its ...

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  11. If veca, vecb, vecc are unit vectors, then |veca-vecb|^2+|vecb-vec|^2+...

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  12. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

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  13. Let vec A(t) = f1(t) hat i + f2(t) hat j and vec B(t) = g(t)hat i+g2(...

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  14. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  15. Let vecV=2hati+hatj-hatk and vecW=hati+3hatk. It vecU is a unit vector...

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  16. The value of a so that the volume of the paralelopiped formed by hati+...

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  17. A unit vector int eh plane of the vectors 2hati+hatj+hatk, hati-hatj+h...

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  18. If veca=veci+vecj+veck, veca.vecb=1 and vecaxxvecb=vecj-veck, then vec...

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  19. If veca,vecb,vecc,vecd are four distinct vectors satisfying the condit...

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  20. Let veca=hati + 2hatj +hatk, vecb=hati - hatj +hatk andvecc= hathatj-h...

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  21. Let vecA be a vector parallel to the of intersection of planes P1 and ...

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