Advertisements
Advertisements
प्रश्न
Write the distance of the point (3, −5, 12) from X-axis?
उत्तर
\[ \text { The distance of a general point } \left( x, y, z \right) \text{ from x - axis is } \sqrt{y^2 + z^2} . \]
\[ \therefore \text{ Distance of the point } \left( 3, - 5, 12 \right) \text{ from x - axis }= \sqrt{\left( - 5 \right)^2 + {12}^2} \]
\[ = \sqrt{169} \]
\[ = 13 \text{ units }\]
संबंधित प्रश्न
Find the direction cosines of the line
`(x+2)/2=(2y-5)/3; z=-1`
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 makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
(A) `0,1/sqrt2,-1/sqrt2`
(B) `0,-1/sqrt2,-1/sqrt2`
(C) `1,1/sqrt2,1/sqrt2`
(D) `0,-1/sqrt2,1/sqrt2`
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.
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.
Find the angle between the lines whose direction cosines are given by the equations
2l − m + 2n = 0 and mn + nl + lm = 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 X-axis?
If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.
Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question:
Write the distance of a point P(a, b, c) from 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.
The distance of the point P (a, b, c) from the x-axis is
Ratio in which the xy-plane divides the join of (1, 2, 3) and (4, 2, 1) is
If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio
Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) .
Verify whether the following ratios are direction cosines of some vector or not
`4/3, 0, 3/4`
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`
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
`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 the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
P is a point on the line segment joining the points (3, 2, –1) and (6, 2, –2). If x co-ordinate of P is 5, then its y co-ordinate is ______.
If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.
A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.
If a line makes angles `pi/2, 3/4 pi` and `pi/4` with x, y, z axis, respectively, then its direction cosines are ______.
Find the equations of the two lines through the origin which intersect the line `(x - 3)/2 = (y - 3)/1 = z/1` at angles of `pi/3` each.
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 projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are ______.
Equation of line passing through origin and making 30°, 60° and 90° with x, y, z axes respectively, is ______.
If the equation of a line is x = ay + b, z = cy + d, then find the direction ratios of the line and a point on the line.
If a line makes an angle α, β and γ with positive direction of the coordinate axes, then the value of sin2α + sin2β + sin2γ will be ______.
