Advertisements
Advertisements
प्रश्न
The distance of the point P (a, b, c) from the x-axis is
विकल्प
\[\sqrt{b^2 + c^2}\]
\[\sqrt{a^2 + c^2}\]
\[\sqrt{a^2 + b^2}\]
none of these
Advertisements
उत्तर
\[\left( a \right) \sqrt{b^2 + c^2}\]
\[\text{ The projection of the point P } \left( a, b, c \right) \text{ on the x - axis is } \left( a, 0, 0 \right) \text{ as both Y and Z coordinates on any point on the x - axis are equal to zero } . \]
\[ \therefore \text{ Distance of P } \left( a, b, c \right) \text{ from x - axis = Distance of P } \left( a, b, c \right) \text{ from } \left( a, 0, 0 \right)\]
\[ = \sqrt{\left( a - a \right)^2 + \left( b - 0 \right)^2 + \left( c - 0 \right)^2}\]
\[ = \sqrt{b^2 + c^2}\]
APPEARS IN
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`
If a line has the direction ratios −18, 12, −4, then what are its direction cosines?
Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.
Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.
Show that the line through points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (−1, −2, 1) and (1, 2, 5).
Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).
If the coordinates of the points A, B, C, D are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2), then find the angle between AB and CD.
Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.
Find the angle between the lines whose direction cosines are given by the equations
(i) l + m + n = 0 and l2 + m2 − n2 = 0
Find the angle between the lines whose direction cosines are given by the equations
2l − m + 2n = 0 and mn + nl + lm = 0
What are the direction cosines of X-axis?
What are the direction cosines of Y-axis?
Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.
Find the distance of the point (2, 3, 4) from the x-axis.
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
For every point P (x, y, z) on the x-axis (except the origin),
A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is
The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)
The angle between the two diagonals of a cube is
Verify whether the following ratios are direction cosines of some vector or not
`1/sqrt(2), 1/2, 1/2`
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
Choose the correct alternative:
The unit vector parallel to the resultant of the vectors `hat"i" + hat"j" - hat"k"` and `hat"i" - 2hat"j" + hat"k"` is
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
The vector equation of the line passing through the points (3, 5, 4) and (5, 8, 11) is `vec"r" = 3hat"i" + 5hat"j" + 4hat"k" + lambda(2hat"i" + 3hat"j" + 7hat"k")`
If the directions cosines of a line are k,k,k, then ______.
The area of the quadrilateral ABCD, where A(0,4,1), B(2, 3, –1), C(4, 5, 0) and D(2, 6, 2), is equal to ______.
If two straight lines whose direction cosines are given by the relations l + m – n = 0, 3l2 + m2 + cnl = 0 are parallel, then the positive value of c is ______.
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 a line passing through point (1, 2, 3) and equally inclined to the coordinate axis, is ______.
A directed line makes angles \[\alpha\], \[\beta\], and \[\gamma\] with the positive x-, y-, and z-axes respectively. What are these angles called?
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 \[(l,m,n)\]?
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?
A line passes through \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\]. Which is one set of direction ratios of the line?
