मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the coordinates of the point which is located in the YZ-plane, one unit to the right of the XZ- plane and six units above the XY-plane. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find the coordinates of the point which is located in the YZ-plane, one unit to the right of the XZ- plane, and six units above the XY-plane.

बेरीज

उत्तर

Let the coordinates of the point be (x, y, z). Since the point is located in the YZ plane, x0. Also, the point is one unit to the right of XZ-plane and six units above the XY-plane.
∴ y = 1, z = 6

Hence, coordinates of the required point are (0,1, 6).

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Vectors - Exercise 5.1 [पृष्ठ १५२]

संबंधित प्रश्‍न

If `veca=xhati+2hatj-zhatk and vecb=3hati-yhatj+hatk` are two equal vectors ,then write the value of x+y+z


if `veca = 2hati - hatj - 2hatk " and " vecb = 7hati + 2hatj - 3hatk`, , then express `vecb` in the form of `vecb = vec(b_1) + vec(b_2)`, where `vec(b_1)`  is parallel to `veca` and `vec(b_2)` is perpendicular to `veca`


If \[\overrightarrow{a}\] is a non-zero vector of modulus a and m is a non-zero scalar such that m \[\overrightarrow{a}\] is a unit vector, write the value of m.


Find a unit vector in the direction of \[\overrightarrow{a} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k}\].


For what value of 'a' the vectors \[2 \hat{i} - 3 \hat{j} + 4 \hat{k} \text{ and }a \hat{i} + 6 \hat{j} - 8 \hat{k}\]  are collinear?


If \[\left| \overrightarrow{a} \right| = 4\] and \[- 3 \leq \lambda \leq 2\], then write the range of \[\left| \lambda \vec{a} \right|\].


If \[\vec{a} , \vec{b}\] are the vectors forming consecutive sides of a regular hexagon ABCDEF, then the vector representing side CD is 


Forces 3 O \[\vec{A}\], 5 O \[\vec{B}\] act along OA and OB. If their resultant passes through C on AB, then 


Find the components along the coordinate axes of the position vector of the following point :

S(4, –3)


In Figure, which of the following is not true?


Show that the four points having position vectors

\[6 \hat { i} - 7 \hat { j} , 16 \hat {i} - 19 \hat {j}- 4 \hat {k} , 3 \hat {j} - 6 \hat {k} , 2 \hat {i} + 5 \hat {j} + 10 \hat {k}\] are not coplanar.


ABCDEF is a regular hexagon. Show that `bar"AB" + bar"AC" + bar"AD" + bar"AE" + bar"AF" = 6bar"AO"`, where O is the centre of the hexagon.


Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj + 2hatk` and `3hati + 4hatk` form a triangle or not.


Find a vector in the direction of `bara = hati - 2hatj` that has magnitude 7 units.


Find the distance from (4, - 2, 6) to each of the following:
(a) The XY-plane
(b) The YZ-plane
(c) The XZ-plane
(d) The X-axis
(e) The Y-axis
(f) The Z-axis.


If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is ______.


Select the correct option from the given alternatives:

If `bar"a"  "and"  bar"b"` are unit vectors, then what is the angle between `bar"a"` and `bar"b"` for `sqrt3bar"a" - bar"b"` to be a unit vector?


Find the component form of `bar"a"` if it lies in YZ-plane makes 60° with positive Y-axis and `|bar"a"| = 4`.


A point P with position vector `(- 14hat"i" + 39hat"j" + 28hat"k")/5` divides the line joining A (1, 6, 5) and B in the ratio 3 : 2, then find the point B.


ABCD is a parallelogram. E, F are the midpoints of BC and CD respectively. AE, AF meet the diagonal BD at Q and P respectively. Show that P and Q trisect DB.


If a parallelogram is constructed on the vectors `bar"a" = 3bar"p" - bar"q", bar"b" = bar"p" + 3bar"q" and |bar"p"| = |bar"q"| = 2` and angle between `bar"p" and bar"q"` is `pi/3,` and angle between lengths of the sides is `sqrt7 : sqrt13`.


Let bar"b" = 4hat"i" + 3hat"j" and bar"c" be two vectors perpendicular to each other in the XY-plane. Find the vector in the same plane having projection 1 and 2 along bar"b" and bar"c" respectively.


Find a unit vector perpendicular to the plane containing the point (a, 0, 0), (0, b, 0) and (0, 0, c). What is the area of the triangle with these vertices?


State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:

`bar"a" xx (bar"b".bar"c")`


State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:

`(bar"a".bar"b").bar"c"`


For any non zero vector, a, b, c a · ((b + c) × (a + b + c)] = ______.


If the vectors `overlinea = 2hati - qhatj + 3hatk` and `overlineb = 4hati - 5hatj + 6hatk` are collinear, then the value of q is ______


The values of k for which `|"k"vec"a"| < |vec"a"|` and `"k"vec"a" + 1/2 vec"a"` is parallel to `vec"a"` holds true are ______.


Classify the following measures as scalar and vector.

10-19 coulomb


Classify the following measures as scalar and vector.

20 m/s2


Let `veca, vecb` and `vecc` be three unit vectors such that `veca xx (vecb xx vecc) = sqrt(3)/2 (vecb + vecc)`. If `vecb` is not parallel to `vecc`, then the angle between `veca` and `vecc` is


Four vectors `veca, vecb, vecc` and `vecx` satisfy the relation `(veca.vecx)vecb = vecc + vecx` where `vecb * veca` ≠ 1. The value of `vecx` in terms of `veca, vecb` and `vecc` is equal to


Find `|veca xx vecb|`, if `veca = hati - 7hatj + 7hatk` and  `vecb = 3hati - 2hatj + 2hatk`


The angles of a triangle, two of whose sides are represented by the vectors `sqrt(3)(veca xx vecb)` and `vecb - (veca.vecb)veca` where `vecb` is a non-zero vector and `veca` is a unit vector are ______.


In the triangle PQR, `bar(PQ)=2bara` and `bar(QR)=2barb`. The mid-point of PR is M. Find following vectors in terms of `bara and barb`.

(i) `bar(PR)`  (ii) `bar(PM)`  (iii) `bar(QM)`


In the triangle PQR, `bar"PQ" = 2 bar" a" and bar"QR" = 2 bar"b"`. The midpoint of PR is M. Find the following vectors in terms of `bar"a"` and `bar"b"`:

(i) `bar"PR"` (ii) `bar"PM"` (iii) `bar"QM"`


In the triangle PQR, `bar(PQ) = 2bara and bar(QR) = 2barb`. The mid-point of PR is M. Find the following vectors in terms of `bara and barb`.  

  1. `bar(PR)`
  2. `bar(PM)`
  3. `bar(QM)`

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×