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प्रश्न
Write the distance of the point P (x, y, z) from XOY plane.
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उत्तर
The distance of the point P (x, y, z) from the XOY plane is |z|.
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संबंधित प्रश्न
Which of the following represents direction cosines of the line :
(a)`0,1/sqrt2,1/2`
(b)`0,-sqrt3/2,1/sqrt2`
(c)`0,sqrt3/2,1/2`
(d)`1/2,1/2,1/2`
Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1.
If a line has direction ratios 2, −1, −2, determine its direction cosines.
Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
Show that the line through the points (1, −1, 2) and (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
Find the angle between the lines whose direction ratios are proportional to a, b, c and b − c, c − a, a− b.
Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.
Write the distances of the point (7, −2, 3) from XY, YZ and XZ-planes.
Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.
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If a line makes angles 90°, 135°, 45° with the x, y and z axes respectively, find its direction cosines.
Find the direction cosines of a vector whose direction ratios are
0, 0, 7
Find the direction cosines and direction ratios for the following vector
`hat"j"`
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Choose the correct alternative:
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O is the origin and A is (a, b, c). Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.
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The line `vec"r" = 2hat"i" - 3hat"j" - hat"k" + lambda(hat"i" - hat"j" + 2hat"k")` lies in the plane `vec"r".(3hat"i" + hat"j" - hat"k") + 2` = 0.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.
A line in the 3-dimensional space makes an angle θ `(0 < θ ≤ π/2)` with both the x and y axes. Then the set of all values of θ is the interval ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.
If \[\alpha\], \[\beta\], and \[\gamma\] are the direction angles of a line, which ordered triple gives its direction cosines?
Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?
For direction ratios \[(a,b,c)\], which set can represent the corresponding direction cosines when the direction of the line is chosen?
In the relation between direction ratios and direction cosines, what does the sign \[\pm\] in \[l=\pm\frac{a}{\sqrt{a^2+b^2+c^2}}\] depend on?
For points \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\], which expression gives \[PQ\]?
