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If vec(r )=x hat(i)+y hat(j)+x hat(k), f...

If `vec(r )=x hat(i)+y hat(j)+x hat(k)`, find : `(vec(r )xx hat(i)).(vec(r )xx hat(j))+xy`.

A

0

B

1

C

xy

D

`ixxj`

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Find ( vec (a) xxvec (b)) and |vec(a) xx vec (b)| ,when (i) vec(a) = hat(i)-hat(j)+ 2hat(k) and vec(b)= 2 hat(i)+3 hat(j)-4hat(k) (ii) vec(a)= 2hat (i)+hat(j)+ 3hat(k) and vec(b)= 3hat(i)+5 hat(j) - 2 hat(k) (iii) vec(a)=hat(i)- 7 hat(j)+ 7hat(k) and vec(b) = 3 hat(i)-2hat(j)+2 hat(k) (iv) vec(a)= 4hat(i)+ hat(j)- 2hat(k) and vec(b) = 3 hat(i)+hat(k) (v) vec(a) = 3 hat(i) + 4 hat(j) and vec(b) = hat(i)+hat(j)+hat(k)

If vec(a) = (hat(i) - 2 hat(j)+ 3 hat(k)) and vec(b) = (2 hat(i) + 3 hat(j)- 5 hat(k)) then find (vec(a) xx vec(b)) and " verify that " (vec(a) xx vec(b)) is perpendicular to each one of vec(a) and vec(b) .

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If vec(a) = 3 hat(i) + 2 hat(k) , vec(b) = 3hat(j) - hat(k) and vec(c ) = hat(i) + hat(j) + hat(k) . Find ( vec(a) xx vec(b)). vec(c ) .

ML KHANNA-ADDITION AND MULTIPLICATION OF VECTORS -Problem Set (2) (MULTIPLE CHOICE QUESTIONS)
  1. If A = 2i + 2j-k, B=6i-3j+k,then AxxB will b given by

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  2. If alpha = 2i + 3j - k, beta = -i + 2j-4k, gamma = i+j+k then the valu...

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  3. If vec(r )=x hat(i)+y hat(j)+x hat(k), find : (vec(r )xx hat(i)).(vec...

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  4. If the vectors vec c , vec a=x hat i+y hat j+z hat ka n d vec b= hat ...

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  5. The vector a, b, c are equal in length and taken pairwise they mak equ...

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  6. vecA = (1, -1, 1), vecC = (-1,-1,0) are given vectors then the vector ...

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  7. The vector vecB = 3j + 4k is to be written as the sum of a vector vecB...

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  8. (3)/(2)(i+j)

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  9. and vecB(2) is

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  10. Let the position vectors of the points P, A and B be r,i+j+k and -i+k....

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  11. If a xx b = c xx b ne 0, then

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  12. a xx b = a xx c where (a ne 0) implies that

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  13. If a, b, c be non-zero vectors, then which of the following statements...

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  14. Three points with position vectors, a, b, c are collinear if

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  15. theta is the angle between two vectors a and b then a. b le 0 only if

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  16. If a, b, c be three non-zero vectors, then the equation a. b = a. c ...

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  17. If a. b = a . C and axx b = a xx c, then

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  18. If vec(a) and vec(b) are two vectors such that vec(a).vec(b) = 0 and v...

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  19. If a xx b = c and b xx c = a , then

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  20. If a.b = b.c = c.a = 0, then a.(bxxc)=

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