First slide

Algebra of vectors

Question

If A, B, C and D are position vectors $\vec{a}, \vec{b}, \vec{c} and \vec{d},$ respectively, such that $\vec{a} - \vec{b} = 2 (\vec{d} - \vec{c}) .$ Then

Easy

A

AB and CD bisect each other
B

BD and AC bisect each other
C

AB and CD trisect each other
D

BD and AC trisect each other

Solution

$\begin{array}{l} \vec{a} - \vec{b} = 2 (\vec{d} - \vec{c}) \\ ∴ \frac{\vec{a} + 2 \vec{c}}{2 + 1} = \frac{\vec{b} + 2 \vec{d}}{2 + 1} \end{array}$
Hence, AC and.BD trisect each other as L.H.S. is the position vector of a point trisecting A an C, and R.H.S. that of B and D.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App