मराठी

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.

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

APPEARS IN

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

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

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`


Write the direction ratios of the following line :

`x = −3, (y−4)/3 =( 2 −z)/1`


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 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?


Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).


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.


Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.


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


Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, −1) and (4, 3, −1).


Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.


What are the direction cosines of X-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 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,

 


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


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


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


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

`4/3, 0, 3/4`


Find the direction cosines and direction ratios for the following vector

`hat"i" - hat"k"`


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


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 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.


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 


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.


If a line has the direction ratio – 18, 12, – 4, then what are its direction cosine.


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


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


Which proportion correctly expresses the relationship between direction ratios \[(a,b,c)\] and direction cosines \[(l,m,n)\]?


In the relation between direction ratios and direction cosines, what does the sign \[\pm\] in \[l=\pm\frac{a}{\sqrt{a^2+b^2+c^2}}\] depend on?


A line passes through \[P(x_1,y_1,z_1)\] and \[Q(x_2,y_2,z_2)\]. Which is one set of direction ratios of the line?


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