हिंदी

Write the Distance of the Point (3, −5, 12) from X-axis?

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

\[ \text { The distance of a general point } \left( x, y, z \right) \text{ from  x - axis is } \sqrt{y^2 + z^2} . \]

\[ \therefore \text{ Distance of the point } \left( 3, - 5, 12 \right) \text{ from x - axis }= \sqrt{\left( - 5 \right)^2 + {12}^2} \]

                                      \[ = \sqrt{169} \]

                                      \[ = 13 \text{ units }\]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 26: Direction Cosines and Direction Ratios - Very Short Answers [पृष्ठ २४]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 26 Direction Cosines and Direction Ratios
Very Short Answers | Q 6 | पृष्ठ २४

संबंधित प्रश्न

Find the direction cosines of the line 

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


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


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


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 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 direction cosines of the line passing through two points (−2, 4, −5) and (1, 2, 3) .


Using direction ratios show that the points A (2, 3, −4), B (1, −2, 3) and C (3, 8, −11) are collinear.


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


Show that the line through points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (−1, −2, 1) and (1, 2, 5).


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.


Define direction cosines of a directed line.


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


Write the coordinates of the projection of point P (x, y, z) on XOZ-plane.


If a line has direction ratios proportional to 2, −1, −2, then what are its direction consines?


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 O is the origin, OP = 3 with direction ratios proportional to −1, 2, −2 then the coordinates of P 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"j"`


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 (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


If `vec"a" = 2hat"i" + 3hat"j" - 4hat"k", vec"b" = 3hat"i" - 4hat"j" - 5hat"k"`, and `vec"c" = -3hat"i" + 2hat"j" + 3hat"k"`,  find the magnitude and direction cosines of `3vec"a"- 2vec"b"+ 5vec"c"`


If the direction ratios of a line are 1, 1, 2, find the direction cosines of the line.


If a line makes an angle of 30°, 60°, 90° with the positive direction of x, y, z-axes, respectively, then find its direction cosines.


If a line makes an angle of `pi/4` with each of y and z-axis, then the angle which it makes with x-axis 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")`


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


The Cartesian equation of a line AB is: `(2x - 1)/2 = (y + 2)/2 = (z - 3)/3`. Find the direction cosines of a line parallel to line AB.


The co-ordinates of the point where the line joining the points (2, –3, 1), (3, –4, –5) cuts the plane 2x + y + z = 7 are ______.


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 a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are ______.


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?


For the line directed from \[P(x_1,y_1,z_1)\] to \[Q(x_2,y_2,z_2)\], which expression is the direction cosine \[m\]?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×