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Let veca=a(1)hati+a(2)hatj+a(3)hatk, vec...

Let `veca=a_(1)hati+a_(2)hatj+a_(3)hatk, vecb=b_(1)hati+b_(2)hatj+b_(3)hatk` and `vecc=c_(1)hati+c_(2)hatj+c_(3)hatk` be three non zero vectors such that `vecc` is a unit vector perpendicular to both `veca` and `vecb` . If the angle between `veca` and `vecb` is `(pi)/6`, then `|(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3))|^(2)` is equal to

A

0

B

1

C

`(1/4)(sum_(i=1)^(3)a_(i)^(2))(sum_(i=1)^(3)b_(i)^(2))`

D

none of these

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C
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Let veca=a_(1)hati+a_(2)hatj+a_(3)hatk,vecb=b_(2)hatj+b_(3)hatk and vecc=c_(1)hati+c_(2)hatj+c_(3)hatk gve three non-zero vectors such that vecc is a unit vector perpendicular to both veca and vecb . If the angle between veca and vecb is pi/6 , then prove that |{:(a_(1),a_(2),a_(3)),(b_(1),b_(2),b_(3)),(c_(1),c_(2),c_(3)):}|p=1/4 (a_(1)^(2)+a_(2)^(2)+a_(3)^(2))(b_(1)^(2)+b_(2)^(2)+b_(3)^(2))

Let overset(to)(a) =a_(1) hat(i) + a_(2) hat(j) + a_(3) hat(k) , overset(to)(a) = b_(1) hat(i) +b_(2) hat(j) +b_(3) hat(k) " and " overset(to)(a) = c_(1) hat(i) +c_(2) hat(j) + c_(3) hat(k) be three non- zero vectors such that overset(to)(c ) is a unit vectors perpendicular to both the vectors overset(to)(c ) and overset(to)(b) . If the angle between overset(to)(a) " and " overset(to)(n) is (pi)/(6) then |{:(a_(1),,a_(2),,a_(3)),(b_(1),,b_(2),,b_(3)),(c_(1),,c_(2),,c_(3)):}| is equal to

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

If veca=2hati+3hatj+6hatk and vecb=6hati+3hatj-2hatk , find the angle, between vectors veca and vecb . Also find unit vector perpendicular to both veca and vecb

Let veca = a_1hati + a_2hatj + a_3hatk, vecb = b_1hati + b_2hatj+ b_3hatk and vecc = c_1hati + c_2hatj + c_3hatk be three non zero vectors such that |vecc| =1 angle between veca and vecb is pi/4 and vecc is perpendicular to veca and vecb then |[a_1, b_1, c_1], [a_2, b_2, c_2], [a_3, b_3, c_3]|^2= lamda(a_1 ^2 +a_2 ^2 + a_3 ^2)(b_1 ^2 + b_2^2+b_3^2) where lamda is equal to (A) 1/2 (B) 1/4 (C) 1 (D) 2

Let veca =hati + hatj + sqrt2 hatk, vecb = b_(1) hati + b _(2) hatj + sqrt2 hatk and vecc = 5 hati + hatj + sqrt2 hatk be three vectors such that the projection vector of vecb on veca is veca. If veca + vecb perpendicular to vecc, then |vecb| is equal to

If veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk and vecc=rhati+hatj+(2r-1)hatk are three vectors such that vecc is parallel to the plane of veca and vecb then r is equal to,

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

MCGROW HILL PUBLICATION-VECTOR ALGEBRA-EXERCISE (Level-2 Single Correct Answer Type Questions)
  1. The point of intersection of the lines r times a=b times a, r times b=...

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  2. If a=a(1)i+a(2)j+a(3)k, b=b(1)i+b(2)j+b(3)k, c=c(1)i+c(2)j+c(3)k, d=d(...

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  3. The value of (b times c)*(a times d)+(c times a)*(b times d)+(a times ...

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  4. The lines r=b-2c+lambda(a+b)" and "r=2b-c+mu(b+c) intersect at the poi...

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  5. If a=i+2j-3k, b=2i+j-k then the vector v satisfying a times v=a times ...

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  6. The value of abs(a times(i timesj))^(2)+abs(a times(j timesk))^(2)+a...

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  7. The locus of a point equidistant from two points with position vectors...

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  8. A vector veca=(x,y,z) makes an obtuse angle with F-axis, and make equa...

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  9. If a times b=c" and "b times c=a, then

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  10. Let OABC be a regular tetrahedron, then angle between edges OA and BC ...

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  11. Let veca=a(1)hati+a(2)hatj+a(3)hatk, vecb=b(1)hati+b(2)hatj+b(3)hatk a...

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  12. The vector vec a has the components 2p and 1 w.r.t. a rectangular ...

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  13. a*((b times c) times (a+(b times c)) is equal to

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  14. If overset(to)(X) "." overset(to)(A) =0, overset(to)(X) "." overset(...

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  15. Given the vectors a=3i-j+5k" and "b=i+2j-3k. A vector c which is perp...

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  16. The unit vector in XOZ plane and making angles 45^@ and 60^@ respectiv...

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  17. If vector vec a+ vec b bisects the angle between vec a and vec b , ...

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  18. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

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  19. A B C D is quadrilateral such that vec A B= vec b , vec A D= vec d , ...

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  20. If vecu=veca-vecb,vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvecv...

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