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The lines vec(r)=hat(i)+hat(j)-hat(k)+la...

The lines `vec(r)=hat(i)+hat(j)-hat(k)+lamda(3hat(i)-hat(j))` and `vec(r)=(4hat(i)-hat(k))+mu(2hat(i)+3hat(k))` -

A

meet in a unique points

B

are skew lines

C

are coplanar

D

are coincident

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The correct Answer is:
A, C
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Show that the lines vec(r)=(hat(i)+hat(j)+hat(k))+t(hat(i)-hat(j)+hat(k)) and vec(r)=(3hat(i)-hat(k))+s(4hat(j)-16hat(k)) intersect and find the position vector of their point of intersection.

A line passes through (2,-1,3) and perpendicular to the lines vec(r)=(hat(i)+hat(j)+hat(k))+lamda(2hat(i)-2hat(j)+hat(k)) and vec(r)=(2hat(i)-hat(j)-3hat(k))+mu(hat(i)+2hat(j)+2hat(k)) . Obtain its vector equation.

Find the angle between the lines vec(r)=(3hat(i)+hat(j)-4hat(k))+t(hat(i)+hat(j)+hat(k)) and vec(r)=(5hat(i)-hat(j))+t'(3hat(i)+2hat(j)+4hat(k))

Find the distance between the lines l_(1) and l_(2) given by vec(r)=(hat(i)+2hat(j)-4hat(k))+lamda(2hat(i)+3hat(j)+6hat(k)) and vec(r)=(3hat(i)+3hat(j)-5hat(k))+mu(2hat(i)+3hat(j)+6hat(k))

Find the angle between the following pair of lines vec(r)=(3hat(i)+2hat(j)-4hat(k))+t(hat(i)+2hat(j)+2hat(k))" and "vec(r)=(hat(i)-2hat(j))+t'(3hat(i)+2hat(j)+6hat(k))

Find the shortest distance between the following pairs of parallel lines whose equations are : vec(r)=(hat(i)+2hat(j)+3hat(k))+t(hat(i)-hat(j)+hat(k)) and vec(r)=(2hat(i)-hat(j)-hat(k))+s(-hat(i)+hat(j)-hat(k))

The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

The shortest distance (in units) between the lines vec(r)=(hat(i)+2hat(j)+4hat(k))+t(5hat(j))" and "vec(r)=(hat(i)+2hat(j)+5hat(k))+s(hat(j)) is

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i+3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.

Let vec(a)=4hat(i)+3hat(j)-hat(k), vec(b)=5hat(i)+2hat(j)+2hat(k), vec(c)=2hat(i)-2hat(j)-3hat(k) " and "vec(d)=4hat(i)-4hat(j)+3hat(k), " prove that " vec(b)-vec(a) " and " vec(d)-vec(c) are parallel and find the ratio of their moduli.

CHHAYA PUBLICATION-STRAIGHT LINE IN THREE DIMENSINAL SPACE -Sample Questions for Competitive Examination
  1. The symmetrical from of the lines x+y+z-1=0 and 4x+y-2z+2=0 are -

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

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

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

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

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

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

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

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

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

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

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

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

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

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