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प्रश्न
Choose correct alternatives :
The lines `x/(1) = y/(2) = z/(3) and (x - 1)/(-2) = (y - 2)/(-4) = (z - 3)/(6)` are
पर्याय
perpendicular
intersecting
skew
coincident
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उत्तर
intesecting
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संबंधित प्रश्न
Find the length of the perpendicular (2, –3, 1) to the line `(x + 1)/(2) = (y - 3)/(3) = (z + 1)/(-1)`.
Find the perpendicular distance of the point (1, 0, 0) from the line `(x - 1)/(2) = (y + 1)/(-3) = (z + 10)/(8)` Also find the co-ordinates of the foot of the perpendicular.
A(1, 0, 4), B(0, -11, 13), C(2, -3, 1) are three points and D is the foot of the perpendicular from A to BC. Find the co-ordinates of D.
If the lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1` intersect each other, then find k.
Find the vector equation of a plane which is at 42 unit distance from the origin and which is normal to the vector `2hati + hatj - 2hatk`.
Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 6y – 3z = 63.
Reduce the equation `bar"r".(3hat"i" + 4hat"j" + 12hat"k")` to normal form and hence find
(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.
Show that the line `bar"r" = (2hat"j" - 3hat"k") + lambda(hat"i" + 2hat"j" + 3hat"k") and bar"r" = (2hat"i" + 6hat"j" + 3hat"k") + mu(2hat"i" + 3hat"j" + 4hat"k")` are coplanar. Find the equation of the plane determined by them.
Find the co-ordinates of the foot of the perpendicular drawn from the point (0, 2, 3) to the line `(x + 3)/(5) = (y - 1)/(2) = (z + 4)/(3)`.
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The length of the perpendicular from (1, 6,3) to the line `x/(1) = (y - 1)/(2) =(z - 2)/(3)`
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Equation of X-axis is ______.
The perpendicular distance of the plane 2x + 3y – z = k from the origin is `sqrt(14)` units, the value of k is ______.
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The equation of the plane passing through (2, -1, 3) and making equal intercepts on the coordinate axes is
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The direction cosines of the normal to the plane 2x – y + 2z = 3 are ______
Find direction cosines of the normal to the plane `bar"r"*(3hat"i" + 4hat"k")` = 5
If the normal to the plane has direction ratios 2, −1, 2 and it’s perpendicular distance from origin is 6, find its equation
Find the perpendicular distance of origin from the plane 6x − 2y + 3z - 7 = 0
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
Find the vector equation of the plane which bisects the segment joining A(2, 3, 6) and B(4, 3, −2) at right angles
If z1 and z2 are z-coordinates of the points of trisection of the segment joining the points A (2, 1, 4), B (–1, 3, 6) then z1 + z2 = ______.
The equation of a plane containing the point (1, - 1, 2) and perpendicular to the planes 2x + 3y - 2z = 5 and x + 2y - 3z = 8 is ______.
If 0 ≤ x < 2π, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0, is ______
The equation of a plane containing the line of intersection of the planes 2x - y - 4 = 0 and y + 2z - 4 = 0 and passing through the point (1, 1, 0) is ______
Equations of planes parallel to the plane x - 2y + 2z + 4 = 0 which are at a distance of one unit from the point (1, 2, 3) are _______.
Equation of plane parallel to ZX-plane and passing through the point (0, 5, 0) is ______
If line `(2x - 4)/lambda = ("y" - 1)/2 = ("z" - 3)/1` and `(x - 1)/1 = (3"y" - 1)/lambda = ("z" - 2)/1` are perpendicular to each other then λ = ______.
The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is ______
If the plane passing through the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) is ax + by + cz = d then a + 2b + 3c = ______.
The equation of the plane passing through the intersection of the planes x + 2y + 3z + 4 = 0 and 4x + 3y + 2z + 1 = 0 and the origin is ______.
The d.r.s of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle `pi/4` with plane x + y = 3, are ______.
If plane x + ay + z = 4 has equal intercepts on axes, then 'a' is equal to ______.
The equation of the 1 plane passing through the points (1, –1, 1), (3, 2, 4) and parallel to Y-axis is ______.
What will be the equation of plane passing through a point (1, 4, – 2) and parallel to the given plane – 2x + y – 3z = 9?
Find the equation of the plane containing the lines `(x - 1)/2 = (y + 1)/-1 = z/3` and `x/2 = (y - 2)/-1 = (z + 1)/3`.
Find the equation of plane which is at a distance of 4 units from the origin and which is normal to the vector `2hati - 2hatj + hatk`.
The coordinates of the foot of the perpendicular from the point P(1, 0, 0) in the line `(x - 1)/2 = (y + 1)/-3 = (z + 10)/8` are ______.
The Cartesian equation of a plane through A (7, 8, 6) and parallel to the XY plane is
