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Find the cartesian equation of the line which is perpendicular to lines `(x)/(2)=(y)/(1)=(z)/(3)` and `(x-3)/(-1)=(y-2)/(3)=(z+5)/(5)` and which passes through the points (1,2,3) and hence convert it to vector form.

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The correct Answer is:
`vec(r)=(hat(i)+2hat(j)+3hat(k))+t(-4hat(i)-13hat(j)+7hat(k))`
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Find the equation of the plane which contains the two parallel line: (x-4)/1 = (y-3)/-4=(z-2)/5 and (x-3)/1 = (y+2)/-4=z/5

Slow that the lines (x-5)/(7)=(y+2)/(-5)=(z)/(1) and (x)/(1)=(y)/(2)=(z)/(3) are perpendicular to each other.

Find the equation of the line passing through the point (-1,2,3) and perpendicular to the lines x/2=(y-1)/(-3)=(z+2)/(-2)a n d(x+3)/(-1)=(y+3)/2=(z-1)/3dot

Find the equation of the plane passing through the line (x-1)/(5)=(y+2)/(6)=(z-3)/(4) and point (4, 3, 7) .

Find the equation of the plane perpendicular to the line (x-1)/2=(y-3)/(-1)=(z-4)/2 and passing through the origin.

Find the equation of the line passing through the intersection (-1,3,-2) and perpendicular to the lines (x)/1=(y)/(2)=(z)/3a n d(x+2)/-3=(y-1)/2=(z+1)/5 dot

Find the equation of the projection of the line (x-1)/(2)=(y+1)/(-1)=(z-3)/(4) on the plane x+2y+z=9 .

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CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Sample Questions for Competitive Examination
  1. Find the cartesian equation of the line which is perpendicular to line...

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  2. The symmetrical from of the lines x+y+z-1=0 and 4x+y-2z+2=0 are -

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  3. The equation of line passing through the point vec(a) parallel to the ...

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  4. The lines vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j)) and vec(r)...

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  5. Consider the lines (x-5)/(3)=(y-7)/(-16)=(z-3)/(7) and (x-9)/(3)=(y-13...

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  6. The distance of the point A(veca) from the line vec(r)=vec(b)+tvec(c)...

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

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  8. If the shortest distance between the lines (x-1)/(1)=(y-1)/(1)=(z-1)/(...

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  9. The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy xy=c^(...

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  10. A line passing through the point (1,1,1) from a tiangle of area sqrt(6...

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  11. The direction cosines of two lines satisfy the relations lamda(l+m)=n ...

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  12. Each question in this section contains statements given in two columns...

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

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

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

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  16. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

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  17. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

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  18. L(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2) ...

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  19. Statement - I: The point A (1,0,7) is the mirror image of the point B(...

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  20. Statement - I : The lines vec(r)=hat(i)+hat(j)-hat(k)+S(3hat(i)-hat(j)...

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