Home
Class 12
MATHS
Fid the condition if lines x=a y+b ,z=c ...

Fid the condition if lines `x=a y+b ,z=c y+da n dx=a^(prime)y+b^(prime), z=c^(prime)y+d '` are perpendicular.

Text Solution

AI Generated Solution

To find the condition under which the lines given by the equations \( x = ay + b \), \( z = cy + d \) and \( x = a'y + b' \), \( z = c'y + d' \) are perpendicular, we can follow these steps: ### Step 1: Identify the direction vectors of the lines The first line can be represented in parametric form as: - \( x = ay + b \) - \( z = cy + d \) From this, we can express the direction vector of the first line as: ...
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos
  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos
  • THREE DIMENSIONAL GEOMETRY

    CENGAGE ENGLISH|Exercise All Questions|294 Videos
  • TRIGONOMETRIC EQUATIONS

    CENGAGE ENGLISH|Exercise Archives (Matrix Match Type)|1 Videos

Similar Questions

Explore conceptually related problems

Prove that the line x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),\ z=c^(prime)y+d^(prime) are perpendicular if aa^(prime) + c c^(prime) + 1=0

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

If the abscissae and the ordinates of two point Aa n dB be the roots of a x^2+b x+c=0a n da^(prime)y^2+b^(prime)y=c^(prime)=0 respectively, show that the equation of the circle described on A B as diameter is a a^(prime)(x^2+y^2)+a^(prime)b x+a b^(prime)y+(c a^(prime)+ca)=0.

Show the condition that the curves a x^2+b y^2=1 and a^(prime)\ x^2+b^(prime)\ y^2=1 Should intersect orthogonally

The two lines x=ay+b,z=cy+d and x=a'y+b', z=c'y +d' are pendicular to each other if

If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0 has perpendicular diagonals, then (a) b^2+c^2=b^('2)+c^('2) (b) c^2+a^2=c^('2)+a^('2) (c) a^2+b^2=a^('2)+b^('2) (d) none of these

If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0 has perpendicular diagonals, then b^2+c^2=b^('2)+c^('2) c^2+a^2=c^('2)+a^('2) a^2+b^2=a^('2)+b^('2) (d) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x) a tx=a is also the normal to y=f(x) a tx=b , then there exists at least one c in (a , b) such that (a)f^(prime)(c)=0 (b) f^(prime)(c)>0 (c) f^(prime)(c)<0 (d) none of these

Let f be a continuous, differentiable, and bijective function. If the tangent to y=f(x)a tx=a is also the normal to y=f(x)a tx=b , then there exists at least one c in (a , b) such that f^(prime)(c)=0 (b) f^(prime)(c)>0 f^(prime)(c)<0 (d) none of these

A parallelepiped S has base points A ,B ,Ca n dD and upper face points A^(prime),B^(prime),C^(prime),a n dD ' . The parallelepiped is compressed by upper face A ' B ' C ' D ' to form a new parallepiped T having upper face points A prime prime,B prime prime,C prime prime and D prime prime . The volume of parallelepiped T is 90 percent of the volume of parallelepiped Sdot Prove that the locus of A" is a plane.