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If the position vectors of A, B, C, D ar...

If the position vectors of A, B, C, D are `3bar(i)+2bar(j)+bar(k), 4bar(i)+5bar(j)+5bar(k), 4bar(i)+2bar(j)-2bar(k), 6bar(i)+5bar(j)-bar(k)` respectively then the position vector of the point of intersection of lines AB and CD is

A

`2bar(i)+bar(j)-3bar(k)`

B

`2bar(i)-bar(j)+3bar(k)`

C

`2bar(i)+bar(j)+3bar(k)`

D

`2bar(i)-bar(j)-3bar(k)`

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The correct Answer is:
D
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The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

Find the value of [bar(i)+bar(j)+bar(k),bar(i)-bar(j),bar(i)+2bar(j)-bar(k)] .

Let bar(a) = 2bar(i) +4bar(j)-5bar(k), bar(b) = bar(i)+bar(j)+bar(k), bar(c ) = bar(j)+2bar(k) . Find the unit vector in the opposite direction of a + b + c

If the point whose position vectors are 3bar(i)-2bar(j)-bar(k), 2bar(i)+3bar(j)-4bar(k), bar(i)+bar(j)-2bar(k), 4bar(i)5bar(j)+lambdabar(k) are coplanar, then show that lambda = -46/7 .

If the points whose position vectors are 3bar(i) -2bar(j)-bar(k), 2bar(i)+3bar(j)-4bar(k), -bar(i)+bar(j)+2bar(k), 4bar(i)+5bar(j)+lambdabar(k) are coplanar, then show that lambda = -146/17 .

If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda .

The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)+4bar(j)+2bar(k) and 4bar(i)+2bar(j)+3bar(k) are the vertices of

AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II
  1. The equation to the altitude of the triangle formed by (1, 1, 1), (1, ...

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  2. If the position vectors of A, B are 2bar(i)-9bar(j)-4bar(k), 6bar(i)-3...

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  3. If the position vectors of A, B, C, D are 3bar(i)+2bar(j)+bar(k), 4bar...

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  4. The lineas r = (6 - 6s) a + (4s - 4) b + (4 - 8s) c and r = (2t - 1) a...

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  5. A point on the line passing through (1, 1, 1) and parallel to (1, -2, ...

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  6. A line passing through the point A(3bar(i)+bar(j)-bar(k)) and parallel...

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  7. The point of intersection of the line passing through bar(i)-2bar(j)-b...

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  8. Statement-I : If two vectors are collinear then those vectors are copl...

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  9. Statement-I : Two non zero, non collinear vectors are linearly indepen...

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  10. The descending order of magnitudes of the vectors A=(i-j)/sqrt(2), B=b...

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  11. If D, E, F are mid points of sides BC, CA, AB of triangle ABC and G is...

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  12. Observe the following statements : Assertion (A) : Three vectors are...

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  13. If the vector bar(a)=2bar(i)+3bar(j)+6bar(k) and bar(b) are collinear ...

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  14. If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) ...

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  15. If the points whose position vectors are 2bar(i)+bar(j)+bar(k), 6bar(i...

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  16. Let bar(b)=bar(i)-2bar(j)+3bar(k), bar(a)=2bar(i)+3bar(j)-bar(k) and b...

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  17. The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)...

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  18. If bar(i)-2bar(j), 3bar(j)+bar(k), lambdabar(i)+3bar(j) are coplanar t...

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  19. If 3bar(i)+3bar(j)+sqrt(3)bar(k), bar(i)+bar(k), sqrt(3)bar(i)+sqrt(3)...

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  20. If bar(a)=bar(i)+4bar(j), bar(b)=2bar(i)-3bar(j) and bar(c)=5bar(i)+9b...

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