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The distance between a point P whose pos...

The distance between a point P whose position vector is `5i +j + 3k` and the line `r = (3i + 7j + k) + t ( j + k)` is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
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The distance between a point P whose position vector is 5bar(i)+bar(j)+3bar(k) and the line bar(r)=(3bar(i)+7bar(j)+bar(k))+t(bar(j)+bar(k))

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Find the position vector of point R which divides the line joining the points P and Q whose position vectors are 2 hat(i) - hat(j) + 3 hat(k) and -5 hat(i) + 2 hat(j) - 5 hat(k) in the ratio 3 : 2 (i) internally (ii) externally.

Show that the following points whose position vectors are given are collinear : (i) 5 hat(i) + 5 hat(k), 2 hat(i) + hat(j) + 3 hat(k) and - 4 hat(i) + 3 hat(j) - hat(k) (ii) - 2 hat(i) + 3 hat(j) + 5 hat(k), hat(i) + 2 hat(j) + 3 hat(k) and 7 hat(i) - hat(k) .

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :

The distance of point B with position vector hat i+2hat j+3hat k from the line passing through the point with position vector 4hat i+2hat j+2hat k and parallel to the vector 2hat i+3hat j+6hat k is :

MCGROW HILL PUBLICATION-VECTOR ALGEBRA-SOLVED EXAMPLES (Level-1 Single Correct Answer Type Questions)
  1. Let u=2i-j+3k" and "a=4i-j+2k. The vector component of u orthogonal to...

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  2. Volume of the tetrahedron with vertices P(-1, 2, 0), Q(2, 1, -3), R(1,...

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  3. The distance between a point P whose position vector is 5i +j + 3k and...

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  4. Let a,b, c be the three vectors such that a.(b + c) = b . (c + a) = c ...

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  5. if veca=2i+2j+3k , vecb=-i+2j+k and vcec=3i+j are such that veca+lambd...

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  6. If abs(a)=2, abs(b)=5" and "abs(a times b)=8" then "abs(a*b) is equal ...

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  7. If a*b=b*c=c*a=0," then [abc] is equal to

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  8. Let vec a , vec ba n d vec c be three non-coplanar vectors and ve...

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  9. The volume of the parallelopiped whose sides are given by overset(...

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  10. The points with position vectors 60 i+3j ,40 i-8j ,a i-52 j are col...

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  11. If abs(a)=2, abs(b)=3, abs(c)=4" and "a+b+c=0 then the value of b*c+c...

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  12. A,B,C,D are four points in space and |bar(AB) times bar(CD) +bar(BC) t...

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  13. Given a=i+j-k, b=-i+2j+k" and "c=-i+2j-k. A unit vector perpendicular ...

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  14. If vec a , vec ba n d vec c are unit coplanar vectors, then the sc...

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  15. If the vectors vec a , vec b ,a n d vec c form the sidesB C ,C Aa n d...

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

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  17. Let barV = 2i + j - k and barW = i + 3k If barU is a unit vector, th...

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  18. A vector c perpendicular to the vectors 2i+3j-k" and "i-2j+3k satisfyi...

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  19. If a, b, c be three units vectors such that a xx (b xx c)=(1/2) b ;...

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  20. If a vector ofmagnitude 50 is collinear with vector vecb = 6 hat i - 8...

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