The vertices A, B, C of triangle ABC have respectively position vectors a→,b→,c→ with respect to a given origin O. Show that the point D where the bisector of ∠A meets BC has position vector d→=βb→+yc→β+γ where β=c→-a→

The vertices A, B, C of triangle ABC have respectively position vectors $\vec{a}, \vec{b}, \vec{c}$ with respect to a given origin O. Show that the point D where the bisector of ∠A meets BC has position vector $\vec{d} = \frac{β \vec{b} + y \vec{c}}{β + γ}$ where $β = |\vec{c} - \vec{a}| < .$

Mixed-up sentence exercise

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The vertices A, B, C of triangle ABC have respectively position vectors a→,b→,c→ with respect to a given origin O. Show that the point D where the bisector of ∠A meets BC has position vector d→=βb→+yc→β+γ where β=c→-a→ < .

Mixed-up sentence exercise

The vertices A, B, C of triangle ABC have respectively position vectors $\vec{a}, \vec{b}, \vec{c}$ with respect to a given origin O. Show that the point D where the bisector of ∠A meets BC has position vector $\vec{d} = \frac{β \vec{b} + y \vec{c}}{β + γ}$ where $β = |\vec{c} - \vec{a}| < .$