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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.

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प्रश्न

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.

योग
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उत्तर

We know that a general point (x, y, z) has distance \[\sqrt{y^2 + z^2}\]  from the x-axis.

∴ Distance of a point P(a, b, c) from x-axis = \[\sqrt{b^2 + c^2}\]

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अध्याय 26: Direction Cosines and Direction Ratios - Very Short Answers [पृष्ठ २५]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 26 Direction Cosines and Direction Ratios
Very Short Answers | Q 20 | पृष्ठ २५

संबंधित प्रश्न

If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.


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`


Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.


Find the direction cosines of a line which makes equal angles with the coordinate axes.


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 acute angle between the lines whose direction ratios are proportional to 2 : 3 : 6 and 1 : 2 : 2.


Show that the points (2, 3, 4), (−1, −2, 1), (5, 8, 7) are collinear.


Find the angle between the lines whose direction cosines are given by the equations
(i) l + m + n = 0 and l2 + m2 − n2 = 0


Write the distance of the point (3, −5, 12) from X-axis?


A line makes an angle of 60° with each of X-axis and Y-axis. Find the acute angle made by the line with Z-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 xy-plane,

 


The xy-plane divides the line joining the points (−1, 3, 4) and (2, −5, 6)


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


The angle between the two diagonals of a cube is


 

 


The direction ratios of the line which is perpendicular to the lines with direction ratios –1, 2, 2 and 0, 2, 1 are _______.


 Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines


Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) . 


Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line `vec("r") = (-2hat"i"+3hat"j") +lambda(2hat"i"-3hat"j"+6hat"k").`Also, find the distance between these two lines.


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/sqrt(2), 1/2, 1/2`


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"`


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 a line makes angles α, β, γ with the positive directions of the coordinate axes, then the value of sin2α + sin2β + sin2γ is ______.


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 line makes angles 90°, 135°, 45° with x, y and z-axis respectively then which of the following will be its direction cosine.


A line passes through the points (6, –7, –1) and (2, –3, 1). The direction cosines of the line so directed that the angle made by it with positive direction of x-axis is acute, are ______.


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.


If \[\alpha\], \[\beta\], and \[\gamma\] are the direction angles of a line, which ordered triple gives its direction cosines?


Any three numbers proportional to the direction cosines of a line are called its:


For direction ratios \[(a,b,c)\], which set can represent the corresponding direction cosines when the direction of the line is chosen?


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