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Find the vector and Cartesian equations of the line passing through the point (–1, –1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z − 2.
Concept: Vector and Cartesian Equations of a Line
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The vector equation of line 2x – 1 = 3y + 2 = z – 2 is ______.
Concept: Vector and Cartesian Equations of a Line
The direction ratios of the line which is perpendicular to the two lines `(x - 7)/(2) = (y + 17)/(-3) = (z - 6)/(1) and (x + 5)/(1) = (y + 3)/(2) = (z - 4)/(-2)` are ______.
Concept: Vector and Cartesian Equations of a Line
Choose correct alternatives :
The shortest distance between the lines `vecr = (hati + 2hatj + hatk) + lambda(hati - hatj + hatk) and vecr = (2hati - hatj - hatk) + μ(2hati + hatj + 2hatk)` is ______.
Concept: Distance Between Skew Lines and Parallel Lines
The direction ratios of the line 3x + 1 = 6y – 2 = 1 – z are ______.
Concept: Distance Between Skew Lines and Parallel Lines
The foot of the perpendicular drawn from the origin to a plane is M(1, 2, 0). Find the vector equation of the plane.
Concept: Vector and Cartesian Equations of a Line
Find the cartesian equation of the plane passing through A(1, 2, 3) and the direction ratios of whose normal are 3, 2, 5.
Concept: Vector and Cartesian Equations of a Line
Find the direction ratios of the line perpendicular to the lines
`(x - 7)/2 = (y + 7)/(-3) = (z - 6)/1` and `(x + 5)/1 = (y + 3)/2 = (z - 6)/(-2)`
Concept: Vector and Cartesian Equations of a Line
If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation
Concept: Equation of a Plane
Find the perpendicular distance of origin from the plane 6x − 2y + 3z - 7 = 0
Concept: Equation of a Plane
Find the acute angle between the lines x = y, z = 0 and x = 0, z = 0
Concept: Angle Between Planes
Find the vector equation of the line passing through the point having position vector `-hat"i"- hat"j" + 2hat"k"` and parallel to the line `bar"r" = (hat"i" + 2hat"j" + 3hat"k") + mu(3hat"i" + 2hat"j" + hat"k")`, µ is a parameter
Concept: Vector and Cartesian Equations of a Line
Find the Cartesian equation of the line passing through (−1, −1, 2) and parallel to the line 2x − 2 = 3y + 1 = 6z – 2
Concept: Vector and Cartesian Equations of a Line
Find the Cartesian equation of the plane passing through the points A(1, 1, 2), B(0, 2, 3) C(4, 5, 6)
Concept: Vector and Cartesian Equations of a Line
Find the equation of the plane passing through the point (7, 8, 6) and parallel to the plane `bar"r"*(6hat"i" + 8hat"j" + 7hat"k")` = 0
Concept: Equation of a Plane
Find m, if the lines `(1 - x)/3 =(7y - 14)/(2"m") = (z - 3)/2` and `(7 - 7x)/(3"m") = (y - 5)/1 = (6 - z)/5` are at right angles
Concept: Vector and Cartesian Equations of a Line
Show that the lines `(x + 1)/(-10) = (y + 3)/(-1) = (z - 4)/(1)` and `(x + 10)/(-1) = (y + 1)/(-3) = (z - 1)/4` intersect each other.also find the coordinates of the point of intersection
Concept: Equation of a Plane
Find the Cartesian and vector equation of the plane which makes intercepts 1, 1, 1 on the coordinate axes
Concept: Vector and Cartesian Equations of a Line
Find the distance between the parallel lines `x/2 = y/-1 = z/2` and `(x - 1)/2 = (y - 1)/-1 = (z - 1)/2`
Concept: Distance Between Skew Lines and Parallel Lines
Find the vector equation of the plane passing through the point A(–1, 2, –5) and parallel to the vectors `4hati - hatj + 3hatk` and `hati + hatj - hatk`.
Concept: Equation of a Plane
