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Choose correct alternatives : Equation of X-axis is ______. - Mathematics and Statistics

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प्रश्न

Choose correct alternatives :

Equation of X-axis is ______.

विकल्प

  • x = y = z

  • y = z

  • y = 0, z = 0

  • x = 0, y = 0

MCQ
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उत्तर

Equation of X-axis is y = 0, z = 0.

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Line and Plane - Miscellaneous Exercise 6 B [पृष्ठ २२४]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 6 Line and Plane
Miscellaneous Exercise 6 B | Q 8 | पृष्ठ २२४

संबंधित प्रश्न

Find the length of the perpendicular (2, –3, 1) to the line `(x + 1)/(2) = (y - 3)/(3) = (z + 1)/(-1)`.


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.


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 ______ 


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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 ______  


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The equation of the plane in which the line `(x - 5)/(4) = (y - 7)/(4) = (z + 3)/(-5) and (x - 8)/(7) = (y - 4)/(1) = (z - 5)/(3)` lie, is


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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 :

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 3y + 6z = 49.


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.


The equation of X axis is ______ 


If the foot of the perpendicular drawn from the origin to the plane is (4, −2, -5), then the equation of the plane is ______ 


The coordinates of the foot of perpendicular drawn from the origin to the plane 2x + y − 2z = 18 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


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


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 ______


Equation of the plane passing through A(-2, 2, 2), B(2, -2, -2) and perpendicular to x + 2y - 3z = 7 is ______ 


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 = ______.


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 ______ 


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 ______.


The equation of the 1 plane passing through the points (1, –1, 1), (3, 2, 4) and parallel to Y-axis is ______.


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 Ix + my + nz = 0 containing the line, `(1 - x)/1 = ("y" + 4)/2 = ("z" + 2)/3`. If plane P divides the line segment AB joining points A(–3, –6, 1) and B(2, 4, –3) in ratio k:1 then the value of k is equal to ______.


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 ______.


What will be the equation of plane passing through a point (1, 4, – 2) and parallel to the given plane – 2x + y – 3z = 9?


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Find the vector equation of the line passing through the point (–2, 1, 4) and perpendicular to the plane `barr*(4hati - 5hatj + 7hatk)` = 15


The perpendicular distance of the plane `bar r. (3 hat i + 4 hat j + 12 hat k) = 78` from the origin is ______.


A mobile tower is situated at the top of a hill. Consider the surface on which the tower stands as a plane having points A(1, 0, 2), B(3, –1, 1) and C(1, 2, 1) on it. The mobile tower is tied with three cables from the points A, B and C such that it stands vertically on the ground. The top of the tower is at point P(2, 3, 1) as shown in the figure below. The foot of the perpendicular from the point P on the plane is at the point `Q(43/29, 77/29, 9/29)`.


Answer the following questions.

  1. Find the equation of the plane containing the points A, B and C.
  2. Find the equation of the line PQ.
  3. Calculate the height of the tower.

The Cartesian equation of a plane through A (7, 8, 6) and parallel to the XY plane is


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