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The line of greatest slope on an incline...

The line of greatest slope on an inclined plane `P_1` is that line in the plane which is perpendicular to the line of intersection of plane `P_1` and a horiontal plane `P_2`.
Q. Assuming the plane `4x-3y+7z=0` to be horizontal, the direction cosines of line greatest slope in the plane `2x+y-5z=0` are

A

`((3)/(sqrt(11)), -(1)/(sqrt(11)), (1)/(sqrt(11)))`

B

`((3)/(sqrt(11)), (1)/(sqrt(11)), -(1)/(sqrt(11)))`

C

`(-(3)/(sqrt(11)), (1)/(sqrt(11)), (1)/(sqrt(11)))`

D

`((1)/(sqrt(11)), -(3)/(sqrt(11)), -(1)/(sqrt(11)))`

Text Solution

Verified by Experts

The correct Answer is:
(a)
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ARIHANT MATHS-THREE DIMENSIONAL COORDINATE SYSTEM-Exercise (Passage Based Questions)
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  2. If a=6hat(i)+7hat(j)+7hat(k), b=3hat(i)+2hat(j)-2hat(k), P(1, 2, 3) ...

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  3. If a=6hat(i)+7hat(j)+7hat(k), b=3hat(i)+2hat(j)-2hat(k), P(1, 2, 3) ...

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  5. A(-2, 2, 3) and B(13, -3, 13) and L is a line through A. Q. Coordina...

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  6. A(-2, 2, 3) and B(13, -3, 13) and L is a line through A. Q. Equation...

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  7. The vector equation of a plane is a relation satisfied by position vec...

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  8. The vector equation of a plane is a relation satisfied by position vec...

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  9. The vector equation of a plane is a relation satisfied by position vec...

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  10. A circle is the locus of a point in a plane such that its distance fro...

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  11. A circle is the locus of a point in a plane such that its distance fro...

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  12. A circle is the locus of a point in a plane such that its distance fro...

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  13. Let A(2, 3, 5), B(-1, 3, 2), C(lambda, 5, mu) are the vertices of a tr...

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  14. Let A(2, 3, 5), B(-1, 3, 2), C(lambda, 5, mu) are the vertices of a tr...

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  15. The line of greatest slope on an inclined plane P1 is that line in the...

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  16. The line of greatest slope on an inclined plane P1 is the line in the ...

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  17. The line of greatest slope on an inclined plane P1 is the line in the ...

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  18. Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2). ...

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  19. Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2). ...

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  20. Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2). ...

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