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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(abc) from x-axis.

योग
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उत्तर

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

∴ Distance of a point P(abc) 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.


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


If a line has the direction ratios −18, 12, −4, then what are its direction cosines?


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 has direction ratios 2, −1, −2, determine 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.


If the coordinates of the points ABCD are (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2), then find the angle between AB and CD.


Find the angle between the lines whose direction cosines are given by the equations
(i) 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


Find the angle between the lines whose direction cosines are given by the equations

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What are the direction cosines of Y-axis?


What are the direction cosines of Z-axis?


Write the ratio in which YZ-plane divides the segment joining P (−2, 5, 9) and Q (3, −2, 4).


If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.


Write the inclination of a line with Z-axis, if its direction ratios are proportional to 0, 1, −1.


Write the distance of the point P (xyz) from XOY plane.


Write direction cosines of a line parallel to z-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.


If the x-coordinate of a point P on the join of Q (2, 2, 1) and R (5, 1, −2) is 4, then its z-coordinate is


If P (3, 2, −4), Q (5, 4, −6) and R (9, 8, −10) are collinear, then R divides PQ in the ratio


Verify whether the following ratios are direction cosines of some vector or not

`1/5, 3/5, 4/5`


Find the direction cosines of a vector whose direction ratios are
0, 0, 7


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`3hat"i" + hat"j" + hat"k"`


Find the direction cosines and direction ratios for the following vector

`3hat"i" - 3hat"k" + 4hat"j"`


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


Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).


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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")`


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.


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.


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.


What will be the value of 'P' so that the lines `(1 - x)/3 = (7y - 14)/(2P) = (z - 3)/2` and `(7 - 7x)/(3P) = (y - 5)/1 = (6 - z)/5` at right angles.


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 ______.


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.


Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.


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