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A line AB is inclined to OX at 45^(@) an...

A line AB is inclined to OX at `45^(@)` and to OY at `60^(@)` and let P be any point on line AB such that OP = 12 units. Then the position vector of 'P' is

A

`12((1)/(2)hati+(1)/(2)hatjpm(1)/(sqrt(2))hatk)`

B

`12((1)/(sqrt2)hati+(1)/(2)hatjpm(1)/(sqrt(2))hatk)`

C

`12((1)/(sqrt2)hati+(1)/(2)hatjpm(1)/(2)hatk)`

D

`12((1)/(2)hati+(1)/(sqrt2)hatjpm(1)/(sqrt2)hatk)`

Text Solution

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The correct Answer is:
C
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TARGET PUBLICATION-THREE DIMENSIONAL GEOMETRY -Critical Thinking
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  2. If P(x,y,z) is a point in space at a distance r from the origin O, the...

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  3. A line AB is inclined to OX at 45^(@) and to OY at 60^(@) and let P be...

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  4. The vector of magnitude 6 which is equally inclined to the co-ordinate...

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  6. Line with direction ratios 1, 1, 1 is

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  7. The angle made by the vector 3hati-4hatj+5hatk with the Z-axis is

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  9. If first two numbers of the direction cosines of a line joining points...

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  10. If the points (2,a,-1),(3,4,b)and(1,-2,3) are collinear, the values of...

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  11. If (1,a,1),(3,-1,2)and(1,a^(2),1) are collinear, then the values of a ...

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  12. Points (-2, 4, 7), (3, -6 -8) and (1, -2, -2) are

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  13. If the angle between the lines whose direction cosines are a,(-2)/(3),...

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  14. The acute angle between the lines having direction ratios 5,4,1 and -3...

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  15. Find the angle between the lines whose direction ratios are: 2,-3,4 ...

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  17. The direction cosines l, m and n of two lines are connected by the rel...

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  18. Find the angle between the line whose direction cosines are given ...

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  19. The direction cosines of a line equally inclined to three mutually per...

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  20. Find the angle between any two diagonals of a cube.

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