If $\to a$ and $\to b$ are the position vectors of points A and B respectively, find the position vector of point C on AB produced such that $\to A C = 3 \to A B$

2 \to a - 3 \to b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 \to a - 2 \to b

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3 \to b - 2 \to a

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

2 \to b - 3 \to a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $3 \to b - 2 \to a$

It is given in the question that $\to A C = 3 \to A B$
$\to B C = \to A C - \to A B$
$\to B C = 3 \to A B - \to A B$ $(\to A C = 3 \to A B)$
$\to B C = 2 \to A B$
Now $\frac{A C}{B C} = \frac{| \to A C |}{| \to B C |} = \frac{| 3 \to A B |}{| 2 \to A B |} = \frac{3}{2} \frac{| \to A B |}{| \to A B |} = \frac{3}{2}$
So C divides AB in the ratio 3:2 externally.
And we know that position vector of point P dividing $\to A B$ externally in the ratio m:n is given by $\frac{m \to B - n \to A}{m - n}$
Therefore the position vector of C is given by,
$\to r = \frac{3 \to b - 2 \to a}{3 - 2} = 3 \to b - 2 \to a$ , which is the correct answer.

Suggest Corrections

Similar questions

Q. If

\to a

and

\to b

are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.

If $\to a and \to b$ are the position vectors of $\to A and \to B$ respectively, then find the position vector of point $\to C i n - - \to B A$ produced such that $- - \to B C = 1.5 - - \to B A$ .

Q. If

\to a

and

\to b

are position vectors of point s A and B respectively, then the position vector of points of trisection of AB

Q. If A, B, C are three non-collinear points with position vectors

\to a, \to b, \to c

, respectively, then show that the length of the perpendicular from C on AB is

\frac{| (\to a \times \to b) + (\to b \times \to c) + (\to c \times \to a) |}{| \to b - \to a |}

Q. If

\to a

\to b

are the position vectors of A, B respectively, find the position vector of a point C in AB produced such that AC = 3 AB and that a point D in BA produced such that BD = 2 BA.

Join BYJU'S Learning Program

If →a and →b are the position vectors of points A and B respectively, find the position vector of point C on AB produced such that →AC=3→AB

If $\to a$ and $\to b$ are the position vectors of points A and B respectively, find the position vector of point C on AB produced such that $\to A C = 3 \to A B$