Find the components along the coordinate axes of the position vector of each of the following points:
(i) P(3, 2)
(ii) Q(–5, 1)
(iii) R(–11, –9)
(iv) S(4, –3)

Open in App

Solution

(i) Let O be the origin.
The position vector of point P(3,2), $\vec{O P} = 3 \hat{i} + 2 \hat{j}$
Component of $\vec{O P}$ along x-axis = a vector of magnitude 3 having its direction along the positive direction of x-axis.
Component of $\vec{O P}$ along y-axis = a vector of magnitude 2 having its direction along the positive direction of y-axis.

(ii) The position vector of point Q(-5,1), $\vec{O Q} = - 5 \hat{i} + \hat{j}$
Component of $\vec{O Q}$ along x-axis = a vector of magnitude 5 having its direction along the negative direction of x-axis.
Component of $\vec{O Q}$ along y-axis = a vector of magnitude 1 having its direction along the positive direction of y-axis.

(iii) The position vector of point R(-11,-9), $\vec{O R} = - 11 \hat{i} - 9 \hat{j}$
Component of $\vec{O R}$ along x-axis = a vector of magnitude 11 having its direction along the negative direction of x-axis.
Component of $\vec{O R}$ along y-axis = a vector of magnitude 9 having its direction along the negative direction of y-axis.

(iv) The position vector of point S(4,-3), $\vec{O S} = 4 \hat{i} - 3 \hat{j}$
Component of $\vec{O S}$ along x-axis = a vector of magnitude 4 having its direction along the positive direction of x-axis.
Component of $\vec{O S}$ along y-axis = a vector of magnitude 3 having its direction along the negative direction of y-axis.

Suggest Corrections

Similar questions

Q. If the components of the vector on the coordinate axes are

2, 1, 2.

Then length of the vector is

Suppose that p,q and r are three non-coplanar vectors in $R^{3}$ . Let the components of a vector s along p, q and r be 4, 3 and 5 respectively. If the components of this vector s along (-p+q+r), (p-q+r) and (-p-q+r) are $x$ , $y$ and $z$ respectively, then the value of $2 x + y + z$ is ___

Q. On a graph paper draw the coordinate axes X'OX and YOY', and plot each of the following points:
(i) A(4, 3)
(ii) B(2, 6)
(iii) C(−3, 5)
(iv) D(−5, 2)
(v) E(−2, −3)
(vi) F(−5, −3)
(vii) G(5, −4)
(viii) H(3, −3)

Q. A plane meets coordinate axes at P , Q and R respectively such that position vector of centroid of

Δ P Q R

(2^i - 5^j + 8^k)

, then the equation of plane is

Suppose that p,q and r are three non-coplanar vectors in $R^{3}$ . Let the components of a vector s along p, q and r be 4, 3 and 5 respectively. If the components of this vector s along (-p+q+r), (p-q+r) and (-p-q+r) are $x$ , $y$ and $z$ respectively, then the value of $2 x + y + z$ is ___

Join BYJU'S Learning Program

Find the components along the coordinate axes of the position vector of each of the following points: (i) P(3, 2) (ii) Q(–5, 1) (iii) R(–11, –9) (iv) S(4, –3)

Find the components along the coordinate axes of the position vector of each of the following points:
(i) P(3, 2)
(ii) Q(–5, 1)
(iii) R(–11, –9)
(iv) S(4, –3)