The points $A$ and $B$ are equidistant from the origin, $O$ and have position vectors a and b (refer

Question

The points $A$ and $B$ are equidistant from the origin, $O$ and have position vectors a and b (referred to O) such that the acute angle $AOB$ is $\frac{\pi }{4}$. The point $N$ on $AB$ is such that $AN:NB=1:2$ and the point $M$ is the foot of perpendicular of $N$ on $OB$. Show that the position vector of point $M$ is $\frac{\left( 1+\sqrt{2} \right)}{3}\mathbf{b}$.[4] Given that $\mathbf{b}$ is a unit vector, find the exact area of $\Delta OMN$.[4]

Accepted Answer

(i) $\overrightarrow{OM}=\dfrac{1+\sqrt2}{3}\mathbf b$ (ii) $\dfrac{\sqrt2+2}{18}$ units$^2$

2013 SRJC P1 Q8

2013 SRJC P1 Q8

Video Solution:

Solution:

Solution locked