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Let L be the line of intersection of the...

Let `L` be the line of intersection of the planes `2x+3y+z=1a n dx+3y+2z=2.` If `L` makes an angle `alpha` with the positive x-axis, then `cosalpha` equals a. `1/2` b. `1` c. `1/(sqrt(2))` d. `1/(sqrt(3))`

A

`(1)/(2)`

B

1

C

`(1)/(sqrt2)`

D

`(1)/(sqrt3)`

Text Solution

Verified by Experts

The correct Answer is:
d
Since line of intersection is perpendicular to both the planes, direction rations of the line of intersection is ltbgt `|[hati,hatj,hatk],[2,3,1],[1,3,2]|=3hati-3hatj+3hatk`
Hence, `cosalpha=(3)/(sqrt(9+9+9))=(1)/(sqrt3)`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  3. Let L be the line of intersection of the planes 2x+3y+z=1a n dx+3y+2z=...

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  4. The length of the perpendicular drawn from (1,2,3) to the line (x-6...

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  5. If the angle theta between the line (x+1)/1=(y-1)/2=(z-2)/2 and the pl...

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  6. The intersection of the spheres x^2+y^2+z^2+7x-2y-z=13a n dx^2+y^2=...

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  7. If a plane cuts off intercepts OA = a, OB = b, OC = c from the coordi...

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  8. A line makes an angel theta with each of the x-and z-axes. If the a...

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  9. The shortest distance from the plane 12 x+y+3z=327 to the sphere x^...

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  10. A tetrahedron has vertices O(0,0,0),A(1,2,1),B(2,1,3),a n dC(-1,1,2), ...

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  11. The radius of the circle in which the sphere x^(I2)+y^2+z^2+2z-2y-4...

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  12. The lines (x-2)/1=(y-3)/2=(z-4)/(-k)a n d=(x-1)/k=(y-4)/2=(z-5)/1 are ...

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  13. The point of intersection of the lines (x-5)/3=(y-7)/(-1)=(z+2)/1a ...

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  14. Two systems of rectangular axes have the same origin. If a plane cu...

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  15. Find the equation of a plane which passes through the point (3, 2, 0...

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  16. The direction ratios of a normal to the plane through (1,0,0)a n d(...

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  17. The centre of the circle given by vecr.(hati+2hatj+2hatk)=15and|vecr-(...

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