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प्रश्न
The equation of X axis is ______
विकल्प
x = y = z
y = z
y = 0, z = 0
x = 0, y = 0
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उत्तर
y = 0, z = 0
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संबंधित प्रश्न
Find the co-ordinates of the foot of the perpendicular drawn from the point `2hati - hatj + 5hatk` to the line `barr = (11hati - 2hatj - 8hatk) + λ(10hati - 4hatj - 11hatk).` Also find the length 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.
Find the perpendicular distance of the origin from the plane 6x – 2y + 3z – 7 = 0.
Find the vector equation of the plane passing through the point having position vector `hati + hatj + hatk` and perpendicular to the vector `4hati + 5hatj + 6hatk`.
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)`.
Choose correct alternatives:
If the line `x/(3) = y/(4)` = z is perpendicular to the line `(x - 1)/k = (y + 2)/(3) = (z - 3)/(k - 1)`, then the value of k 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 the points (1, −1, 1), (3, 2, 4) and parallel to the Y-axis is ______
Choose correct alternatives :
The foot of perpendicular drawn from the point (0,0,0) to the plane is (4, -2, -5) then the equation of the plane is
Solve the following :
Reduce the equation `bar"r".(6hat"i" + 8hat"j" + 24hat"k")` = 13 normal form and hence find
(i) the length of the perpendicular from the origin to the plane.
(ii) direction cosines of the normal.
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
Find the vector equation of a plane at a distance 6 units from the origin and to which vector `2hat"i" - hat"j" + 2hat"k"` is normal
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 the line `(x - 3)/2 = (y + 2)/-1 = (z + 4)/3` lies in the plane lx + my - z = 9, then l2 + m2 is equal to ______
The equation of the plane passing through the point (– 1, 2, 1) and perpendicular to the line joining the points (– 3, 1, 2) and (2, 3, 4) is ______.
Equation of the plane passing through A(-2, 2, 2), B(2, -2, -2) and perpendicular to x + 2y - 3z = 7 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 ______
The intercepts of the plane 3x - 4y + 6z = 48 on the co-ordinate axes are ______
XY-plane divides the line joining the points A(2, 3, -5) and B(1, -2, -3) in the ratio ______
The equation of the plane through (1, 2, -3) and (2, -2, 1) and parallel to the X-axis is ______
The equation of the plane through the point (2, -1, -3) and parallel to the lines `(x - 1)/3 = (y + 2)/2 = z/(-4)` and `x/2 = (y - 1)/(-3) = (z - 2)/2` is ______
A plane which passes through the point (3, 2, 0) and the line `(x - 3)/1 = (y - 6)/5, (z - 4)/4` is ______
If the plane x - 3y + 5z = d passes through the point (1, 2, 4), then the lengths of intercepts cut by it on the axes of X, Y, Z are respectively ______
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 ______.
The equation of the plane passing through a point having position vector`-2hat"i" + 7hat"j" + 5hat"k"` and parallel to the vectors `4hat"i" - hat"j" + 3hat"k"` and `hat"i" + hat"j" + hat"k"` is ______.
If the line `(x + 1)/2 = (y - 5)/3 = (z - "p")/6` lies in the plane 3x – 14y + 6z + 49 = 0, then the value of p is ______.
If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to ______.
Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line `vecr = -hatk + λ(hati + hatj + 2hatk)`, λ ∈ R. Then, which of the following points lies on T?
Let P be a plane passing through the points (1, 0, 1), (1, –2, 1) and (0, 1, –2). Let a vector `vec"a" = αhat"i" + βhat"j" + γhat"k"` be such that `veca` is parallel to the plane P, perpendicular to `(hat"i"+2hat"j"+3hat"k")`and `vec"a".(hat"i" + hat"j" + 2hat"j")` = 2, then (α – β + γ)2 equals ______.
If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is ______.
The equation of the plane passes through the point (2, 5, –3) perpendicular to the plane x + 2y + 2z = 1 and x – 2y + 3z = 4 is ______.
Reduce the equation `barr*(3hati - 4hatj + 12hatk)` = 3 to the normal form and hence find the length of perpendicular from the origin to the plane.
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 ______.
Find the equation of the plane which contains the line of intersection of the planes x + 2y + 4z = 4 and 2x – 3y – z = 9 and which is perpendicular to the plane 4x – 3y + 5z = 10.
Find the point of intersection of the line `(x + 1)/2 = (y - 1)/3 = (z - 2)/1` with the plane x + 2y – z = 6.
Find the equation of the plane containing the line `x/(-2) = (y - 1)/3 = (1 - z)/1` and the point (–1, 0, 2).
