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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

2i + j + 3k

B

2i - j + 3k

C

2i + j + 3k

D

2i - j - 3k

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The correct Answer is:
D
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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

DIPTI PUBLICATION ( AP EAMET)-ADDITION OF VECTORS -EXERCISE 1

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  3. The vector equation to the line passing through the points (-2, 3, 5),...

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  4. The vector equation to the line passing through the points 2i + j + 3k...

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  5. The vector equation to the line passing through the points a + 2b + 3c...

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  6. The cartesian equation of the line passing through the points 2i + j +...

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

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

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  9. Find the equation of the line parallel to the vector 2bar(i)-bar(j)+2b...

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  10. The vector equation of the plane passing through the point 2i + 2j - 3...

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  11. The vector equation of the plane passing through the point (1, -2, -3)...

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  12. The vector equation of the plane passing through the points (1, -2, 5)...

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  13. The vector equation of the plane passing through the points i + 2j + 5...

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  14. Subtract 3a−2b+4c from the sum of −2a+b−5c and 3a−2b+c

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  15. If a, b are two points then r = (1 - p) a + p b represents

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  16. If a, b, c are three noncollinear points then r = (1 - p - q) a + pb +...

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  17. If r = alpha a + beta b + gamma c represents a plane passing through t...

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  18. If r = alpha a + beta b + gamma c represents a plane passing through t...

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  19. The point of intersection of the lines l(1) : r(t) = (i - 6j + 2k) + t...

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  20. P, Q, R and S are four points with the position vectors 3bar(i)-4bar(j...

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