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Direction - cosines of vec(a)=hat(i)+hat...

Direction - cosines of `vec(a)=hat(i)+hat(j)-2hat(k)` are :

A

`lt (1)/(6),(1)/(6),(-2)/(6)gt`

B

`lt (1)/(sqrt(6)),(1)/(sqrt(6)),(-2)/(sqrt(6))gt`

C

`lt sqrt(6), sqrt(6), -sqrt(6)gt`

D

`lt sqrt(6), sqrt(6), (-sqrt(6))/(2)gt`

Text Solution

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The correct Answer is:
B
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Find the unit vector in the direction of the sum of the vectors : vec(a) = 2hat(i)-hat(j)+2hat(k) and vec(b)=-hat(i)+hat(j)+3hat(k) .

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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)

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MODERN PUBLICATION-VECTOR ALGEBRA -Objective Type Questions (A. Multiple Choice Questions)
  1. Direction - ratios of vector vec(a)=hat(i)+hat(j)-2hat(k) are :

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  2. If vec(a)=hat(i)+2hat(j), then |vec(a)| is :

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  3. Direction - cosines of vec(a)=hat(i)+hat(j)-2hat(k) are :

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  4. If p hat(i)+3hat(j) is a vector of magnitude 5, then the value of p is...

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  5. If is the angle between any two vectors vec a and vec b , t...

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  6. The inequality |vec(a).vec(b)|le |vec(a)||vec(b)| is called :

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  7. The vectors vec(a) and vec(b) are perpendicular if :

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  8. Find the angle between two vectors vec a and vec b with magnitudes 1 a...

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  9. Find | vec a- vec b|,\ if:| vec a|=2,\ | vec b|=3\ a n d\ vec adot ve...

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  10. The angle between the vectors : vec(a)=hat(i)+2hat(j)-3hat(k) and 3...

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  11. The D.C.'s of the vector hat(i)+2hat(j)+3hat(k) are :

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  12. If vec(a)=2hat(i)+2hat(j)+3hat(k), then its magnitude is :

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  13. If vec(a) and vec(b) are unlike vectors, then the angle between them i...

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  14. The angle between the vectors hat(i)-hat(j) and hat(j)+hat(k) is :

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  15. If vec(a).vec(b)=|vec(a)xx vec(b)|, then angle between vector vec(a) a...

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  16. Find the projection of the vector hat i+3 hat j+7 hat k on the vecto...

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  17. If the angle between two vectors vec(a) and vec(b) is zero, then :

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  18. The projection of vector vec(a)=2hat(i)+3hat(j)+2hat(k) on vec(b)=hat(...

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  19. If the vectors 5hat(i)+2hat(j)-hat(k) and lambda hat(i)-hat(j)+5hat(k...

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  20. Let the vectors vec a and vec b be such that | vec a|=3 and | ...

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