हिंदी

Define Position Vector of a Point. - Mathematics

Advertisements
Advertisements

प्रश्न

Define position vector of a point.

योग
Advertisements

उत्तर

A point O is fixed as origin in space (or plane) and P is any point, then \[\overrightarrow{OP}\] is called a position vector of P with respect to O.

shaalaa.com
Position Vector of a Point Dividing a Line Segment in a Given Ratio
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: Algebra of Vectors - Very Short Answers [पृष्ठ ७५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 23 Algebra of Vectors
Very Short Answers | Q 3 | पृष्ठ ७५

संबंधित प्रश्न

The two vectors `hatj+hatk " and " 3hati-hatj+4hatk` represent the two sides AB and AC, respectively of a ∆ABC. Find the length of the median through A


Let \[\vec{a,} \vec{b,} \vec{c,} \vec{d}\] be the position vectors of the four distinct points ABCD. If \[\vec{b} - \vec{a} = \vec{c} - \vec{d}\], then show that ABCD is a parallelogram.


Show that the four points P, Q, R, S with position vectors \[\vec{p}\], \[\vec{q}\], \[\vec{r}\], \[\vec{s}\] respectively such that 5 \[\vec{p}\] − 2 \[\vec{q}\] + 6 \[\vec{r}\] − 9 \[\vec{s}\] \[\vec{0}\], are coplanar. Also, find the position vector of the point of intersection of the line segments PR and QS.


Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.


If the position vector of a point (−4, −3) be \[\vec{a,}\] find \[\left| \vec{a} \right|\]


Find the coordinates of the tip of the position vector which is equivalent to \[\vec{A} B\], where the coordinates of A and B are (−1, 3) and (−2, 1) respectively.


If the position vectors of the points A (3, 4), B (5, −6) and C (4, −1) are \[\vec{a,}\] \[\vec{b,}\] \[\vec{c}\] respectively, compute \[\vec{a} + 2 \vec{b} - 3 \vec{c}\].


If \[\vec{a}\] be the position vector whose tip is (5, −3), find the coordinates of a point B such that \[\overrightarrow{AB} =\] \[\vec{a}\], the coordinates of A being (4, −1).


The position vectors of points A, B and C  are \[\lambda \hat{i} +\] 3 \[\hat{j}\],12\[\hat{i} + \mu\] \[\hat{j}\] and 11\[\hat{i} -\] 3 \[\hat{j}\] respectively. If C divides the line segment joining and B in the ratio 3:1, find the values of \[\lambda\] and \[\mu\]


Find a unit vector in the direction of the resultant of the vectors
\[\hat{i} - \hat{j} + 3 \hat{k} , 2 \hat{i} + \hat{j} - 2 \hat{k} \text{ and }\hat{i} + 2 \hat{j} - 2 \hat{k} .\]


If \[\overrightarrow{PQ} = 3 \hat{i} + 2 \hat{j} - \hat{k}\] and the coordinates of P are (1, −1, 2), find the coordinates of Q.


If the vertices of a triangle are the points with position vectors \[a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} , b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k} , c_1 \hat{i} + c_2 \hat{j} + c_3 \hat{k} ,\]
what are the vectors determined by its sides? Find the length of these vectors.


Find the position vector of a point R which divides the line segment joining points \[P \left( \hat{i} + 2 \hat{j} + \hat{k} \right) \text{ and Q }\left( - \hat{i} + \hat{j} + \hat{k} \right)\] internally 2:1.


Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q(4, 1, −2).


Show that the points A, B, C with position vectors \[\vec{a} - 2 \vec{b} + 3 \vec{c} , 2 \vec{a} + 3 \vec{b} - 4 \vec{c}\] and \[- 7 \vec{b} + 10 \vec{c}\] are collinear.


If \[\vec{a,} \vec{b}\] are two non-collinear vectors prove that the points with position vectors \[\vec{a} + \vec{b,} \vec{a} - \vec{b}\text{ and }\vec{a} + \lambda \vec{b}\] are collinear for all real values of λ.


If the points A(m, −1), B(2, 1) and C(4, 5) are collinear, find the value of m.


Show that the points whose position vectors are as given below are collinear: \[3 \hat{i} - 2 \hat{j} + 4 \hat{k}, \hat{i} + \hat{j} + \hat{k}\text{ and }- \hat{i} + 4 \hat{j} - 2 \hat{k}\]


Show that the four points A, B, C and D with position vectors \[\vec{a}\], \[\vec{b}\], \[\vec{c}\], \[\vec{d}\] respectively are coplanar if and only if \[3 \vec{a} - 2 \vec{b} + \vec{c} - 2 \vec{d} = \vec{0} .\]


Find the position vector of the point which divides the join of points with position vectors `vec"a" + 3vec"b" and vec"a"- vec"b"` internally in the ratio 1 : 3. 


X and Y are two points with position vectors `3vec("a") + vec("b")` and `vec("a")-3vec("b")`respectively. Write the position vector of a point Z which divides the line segment XY in the ratio 2 : 1 externally.


Find the value of x such that the four-point with position vectors,
`"A"(3hat"i"+2hat"j"+hat"k"),"B" (4hat"i"+"x"hat"j"+5hat"k"),"c" (4hat"i"+2hat"j"-2hat"k")`and`"D"(6hat"i"+5hat"j"-hat"k")`are coplaner.


Find the position vector of a point R which divides the line joining the two points P and Q with position vectors `vec"OP" = 2vec"a" + vec"b"` and `vec"OQ" = vec"a" - 2vec"b"`, respectively, in the ratio 1:2 externally


The position vector of the point which divides the join of points `2vec"a" - 3vec"b"` and `vec"a" + vec"b"` in the ratio 3:1 is ______.


Position vector of the mid-point of line segment AB is `3hati + 2hatj - 3hatk`. If position vector of the point A is `2hati + 3hatj - 4hatk`, then position vector of the point B is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×