Name: Cross Product
Uploaded: 2019-07-19
Duration: 4 min 16 s
Description: The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a particular direction and magnitude. Watch this vi...

Question

The position vectors of two points

A

and

B

are

\bar{OA} = 2 \hat{i} - \hat{j} - \hat{k}

and

\bar{OB} = 2 \hat{i} - \hat{j} + 2 \hat{k}

, respectively. The position vector of a point

P

which divides the line segment joining

A

and

B

in the ratio

2 : 1

is

Accepted Answer

The position vectors of two points $A$ and $B$ are $\bar{OA} = 2 \hat{i} - \hat{j} - \hat{k}$ and $\bar{OB} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ , respectively.

Let The position vector of a point $P$ which divides the line segment joining $A$ and $B$ in the ratio $2 : 1$ is $\bar{O P}$

When a point whose position vector is $\bar{O P}$ divides the line segment joining the position vectors $\bar{O A}$ and $\bar{O B}$ in the ratio of $m : n$ , then $\bar{O P} = \frac{n \bar{O A} + m \bar{O B}}{m + n}$

$\Rightarrow \bar{O P} = \frac{\bar{O A} + 2 \bar{O B}}{2 + 1}$

$\Rightarrow \bar{O P} = \frac{2 \hat{i} - \hat{j} - \hat{k} + 2 (2 \hat{i} - \hat{j} + 2 \hat{k})}{3}$

$\Rightarrow \bar{O P} = 2 \hat{i} - \hat{j} + \hat{k}$

Thus the required position vector is $2 \hat{i} - \hat{j} + \hat{k}$ .

The position vectors of two points $A$ and $B$ are $\bar{OA} = 2 \hat{i} - \hat{j} - \hat{k}$ and $\bar{OB} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ , respectively. The position vector of a point $P$ which divides the line segment joining $A$ and $B$ in the ratio $2 : 1$ is

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

The position vectors of two points A and B are OA¯=2i^-j^-k^ and OB¯=2i^-j^+2k^, respectively. The position vector of a point P which divides the line segment joining A and B in the ratio 2:1 is

Important Questions on Vector Algebra

Learn and Prepare for any exam you want !

The position vectors of two points $A$ and $B$ are $\bar{OA} = 2 \hat{i} - \hat{j} - \hat{k}$ and $\bar{OB} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ , respectively. The position vector of a point $P$ which divides the line segment joining $A$ and $B$ in the ratio $2 : 1$ is