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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. - Mathematics

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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

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

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आरडी शर्मा Mathematics [English] Class 12
अध्याय 27 Direction Cosines and Direction Ratios
Very Short Answers | Q 20 | पृष्ठ २५

संबंधित प्रश्न

Find the direction cosines of the line 

`(x+2)/2=(2y-5)/3; z=-1`


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


If l1m1n1 and l2m2n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1n1l2 − n2l1l1m2 ­− l2m1.


Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`


If a line has direction ratios 2, −1, −2, determine its direction cosines.


Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.


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


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.


What are the direction cosines of Y-axis?


What are the direction cosines of Z-axis?


Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.


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.


For every point P (xyz) on the xy-plane,

 


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 angle between the two diagonals of a cube is


 

 


If a line makes angles α, β, γ, δ with four diagonals of a cube, then cos2 α + cos2 β + cos2γ + cos2 δ is equal to


 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) . 


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

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


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


A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians


If `1/2, 1/sqrt(2), "a"` are the direction cosines of some vector, then find a


If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c


The x-coordinate of a point on the line joining the points Q(2, 2, 1) and R(5, 1, –2) is 4. Find its z-coordinate.


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 ______.


If the directions cosines of a line are k,k,k, then ______.


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.


The d.c's of a line whose direction ratios are 2, 3, –6, are ______.


The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector 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 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 ______.


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