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vec(a)=hati+hatj+hatk,vec(b)=hati-hatj+h...

`vec(a)=hati+hatj+hatk,vec(b)=hati-hatj+hatk`
and `vec( c )=hati+2hatj-hatk` then the value of
`|{:(vec(a).vec(b),vec(a).vec(b),vec(a).vec( c )),(vec(b).vec(a),vec(b).vec(a),vec(b).vec( c )),(vec( c ).vec(a),vec( c ).vec(b),vec( c ).vec( c )):}|` is .............

A

2

B

4

C

16

D

64

Text Solution

Verified by Experts

The correct Answer is:
C
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If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+hatj+2hatk then find vec(a).(vec(b)xx vec( c )) .

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vec(a)=2hati-10hatj+2hatk,vec(b)=3hati+hatj+2hatk and vec( c )=2hati+hatj+3hatk then find vec(a)xx(vec(b)xxvec( c )) .

vec(a)=2hati-2hatj+hatk,vec(b)=hati+2hatj-2hatk and vec( c )=2hati-hatj+4hatk then find the projection of vec(b)+vec( c ) on vec(a) .

Prove that [vec(a)+vec(b), vec(b)+vec( c ), vec( c )+vec(a)]=2[vec(a),vec(b),vec( c )] .

If vec(a)=3hati-hatj+2hatk,vec(b)=hati-3hatk and vec( c )=hati+2hatj then find (i) vec(a).vec(b) (ii) (vec(a)+vec(b)).vec( c ) (iii) (vec(a)-vec(b)).(vec(b)-vec( c )) (iv) (vec(a)+2vec(b)).vec(b) (v) (vec(a)-3vec( c )).(2vec(a)+vec(b))

If vec(a)=hati+hatj+2hatk and vec(b)=3hati+2hatj-hatk then find vec(a)+3vec(b).(2vec(a)-vec(b)) .

Prove that [vec(a),vec(b),vec( c )+vec(d)]=[vec(a),vec(b),vec( c )]+[vec(a),vec(b),vec(d)] .

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KUMAR PRAKASHAN-VECTOR ALGEBRA -Solutions of NCERT Exemplar Problems (Multiple Choice Questions (MCQs) )
  1. The position vector of the point P is (4, 5, -3). The distance of the ...

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  2. The position vector of a point A is (4, 2, -3). If the distance of the...

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

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  4. A(1, 1, 2), B(4, 3, 1) and C(2, 3, 5) are vertices of a triangle ABC. ...

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  5. The position vectors of two points A and B are respectively 6vec(a)+2v...

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  6. The position vectors of the vertices of triangle are 3hati+4hatj+5hatk...

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  7. The angle between the unit vectors vec(a) and vec(b) is 2theta. Where ...

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  8. squareABCD is a parallelogram. (A(1)) and B(1) are midpoints of the si...

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  9. In DeltaABC,vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk. Length ...

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  10. If bar(x)=(a,4,2a) and bar(y)=(2a,-1,a) are perpendicualr to each othe...

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  11. If bar(x)=(3,1,0),bar(y)=(2,2,3),bar(z)=(-1,2,1). If bar(x)|(bar(y)+...

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  12. If bar(x)=(1,2,4),bar(y)=(-1,-2,k),k ne -4 then |bar(x).bar(y)|………|bar...

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  13. If bar(a)=(-3,1,0) and bar(b)=(1,-1,-1) then "Comp"(bar(a))bar(b) …………...

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  14. The projection of (1, 2, -1) on hati is …………….

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  15. A(3,-1),B(2,3) and C(5,1) are given then m angleA = ………

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  16. bar(x) and bar(y) are unit vectors and (bar(x)""(,)^(hat)bar(y))=theta...

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  17. If |bar(x)+bar(y)|=|bar(x)-bar(y)|, then

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  18. bar(x),bar(y),bar(z) are zero vectors. If …………… then bar(x).bar(y)=bar...

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  19. bar(x),bar(y),bar(z) are non zero vectors. If (bar(x)""(,)^(hat)bar(y)...

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  20. If bar(x).bar(y)=bar(x).bar(z) ne 0 and bar(x)xx bar(y)=bar(x)xx bar(z...

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