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
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Write the direction ratios of the following line :
`x = −3, (y−4)/3 =( 2 −z)/1`
Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.
If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
If a line makes angles of 90°, 60° and 30° with the positive direction of x, y, and z-axis respectively, find its direction cosines
Find the direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .
Find the direction cosines of the sides of the triangle whose vertices are (3, 5, −4), (−1, 1, 2) and (−5, −5, −2).
Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.
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
l + 2m + 3n = 0 and 3lm − 4ln + mn = 0
Find the angle between the lines whose direction cosines are given by the equations
2l + 2m − n = 0, mn + ln + lm = 0
What are the direction cosines of Y-axis?
Write the distance of the point P (x, y, z) from XOY plane.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
If a unit vector `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with } \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.
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
`4/3, 0, 3/4`
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
Find the direction cosines and direction ratios for the following vector
`hat"j"`
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a
If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
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 a variable line in two adjacent positions has direction cosines l, m, n and l + δl, m + δm, n + δn, show that the small angle δθ between the two positions is given by δθ2 = δl2 + δm2 + δn2
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 ______.
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 makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.
Find the direction cosine of a line which makes equal angle with coordinate axes.
If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.
Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.
