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The ratio in which hati + 2 hatj + 3 hat...

The ratio in which `hati + 2 hatj + 3 hatk ` divides the join of `-2hati + 3 hatj + 5 hatk and 7 hati - hatk ,` is

A

`1:2`

B

`2:3`

C

`3:4`

D

`1:4`

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The correct Answer is:
A
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The ratio in which the plane vecr.(hati-2hatj+3hatk)=17 divides the line joining points -2hati+4hatj+7hatk and 3hati-5hatj+8hatk is

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Find the vector and catesian equations of the plane containing the lines : vec(r) = 2 hati + hatj - 3 hatk + lambda (hati + 2 hatj + 5 hatk ) and vec(r) = 3 hati + 3 hatj - 7 hatk + mu (3 hati - 2 hatj + 5 hatk ) .

Find the angle between the following pairs of lines : (i) vec(r) = 2 hati - 5 hatj + hatk + lambda (3 hati + 2 hatj + 6 hatk ) and vec(r) = 7 hati - 6 hatk + mu (hati + 2 hatj + 2 hatk) (ii) vec(r) = 3 hati + hatj - 2 hatk + lambda (hati - hatj - 2 hatk ) and vec(r) = 2 hati - hatj - 56 hatk + mu (3 hati - 5 hatj - 4 hatk) .

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Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

OBJECTIVE RD SHARMA-ALGEBRA OF VECTORS-Chapter Test
  1. In a quadrilateral ABCD, vec(AB) + vec(DC) =

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  2. If ABCDE is a pentagon, then vec(AB) + vec(AE) + vec(BC) + vec(DC) +...

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  3. If ABCD is a parallelogram, then vec(AC) - vec(BD) =

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  4. In a Delta ABC, " if " vec(AB) = hati - 7hatj + hatk and vec(BC) = 3 ...

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  5. In a Delta ABC, if vec(AB) = 3 hati + 4 hatk, vec(AC) = 5 hati + 2 hat...

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  6. The position vectors of P and Q are respectively vec a and vec b . If ...

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  7. If the points whose position vectors are 2hati + hatj + hatk , 6hati -...

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  8. The ratio in which hati + 2 hatj + 3 hatk divides the join of -2hati ...

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  9. If OACB is a parallelogramwith vec(OC) = vec a and vec (AB) = vec b...

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  10. The position vectors of the points A, B, C are 2 hati + hatj - hatk , ...

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  11. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

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  12. If the points with position vectors 20 hati + p hatj , 5 hati - hat...

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  13. If the position vector of a point A is vec a + 2 vec b and vec a divi...

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  14. If vec a ,\ vec b ,\ vec c and vec d are the position vectors of p...

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  15. Let G be the centroid of Delta ABC , If vec(AB) = vec a , vec(AC) = v...

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  16. If G is the intersection of diagonals of a parallelogram ABCD and O is...

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  17. The vector cos alpha cos beta hati + cos alpha sin beta hatj + sin a...

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  18. In a regular hexagon ABCDEF, vecAB=a, vecBC=b and vecCD = c. Then, vec...

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  19. If three points A, B and C have position vectors hati + x hatj + 3 ha...

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  20. If the position vectors of the vertices of a triangle of a triangle ar...

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