Vector Geometry Problems | Mathix (MathGPT)

Vector Parallelogram

1. **Problem statement:** Given a parallelogram ABCD and points M, N, P, Q defined by $$\overrightarrow{AM} = \frac{3}{2} \overrightarrow{AB}, \quad \overrightarrow{BN} = \frac{3}{

Parallelogram Vectors

1. **Problem statement:** We have a parallelogram WXYZ with vectors $\overrightarrow{WX} = \mathbf{u}$ and $\overrightarrow{WZ} = \mathbf{v}$. M is the midpoint of \(\overright

Ratio Zp Zr

1. **State the problem:** We have a parallelogram OXYZ with vectors $\overrightarrow{OX} = a$ and $\overrightarrow{OY} = b$. Points $P$ and $R$ divide $OX$ and $OY$ in

Angle Area Triangle

1. **State the problem:** We are given vectors $\overrightarrow{AB} = -3\mathbf{i} + 6\mathbf{j}$ and $\overrightarrow{AC} = 10\mathbf{i} - 2\mathbf{j}$ in triangle ABC.

Angle Area

1. **Problem statement:** Given vectors $\overrightarrow{AB} = -3i + 6j$ and $\overrightarrow{AC} = 10i - 2j$ in triangle ABC, find: (a) The size of angle $\angle BAC$ in deg

Angle Area Triangle

1. **State the problem:** Given vectors $ \vec{AB} = -3\mathbf{i} + 6\mathbf{j} $ and $ \vec{AC} = 10\mathbf{i} - 2\mathbf{j} $, find: (a) The size of angle $ \angle BAC $ in

Vector Ratios

1. **Stating the problem:** We have triangle OAB with vectors $\mathbf{a} = \overrightarrow{OA}$ and $\mathbf{b} = \overrightarrow{OB}$.

Vector Parallelism

1. Given points and vectors in a coordinate system: $O(0,0)$, $I(1,0)$, $J(0,1)$ with $OI=OJ=1$ cm. 2. Points provided: $A(-3,0)$, $M(3,2)$, and $N(3,-2)$.

Roof Vectors

1. **Problem Statement:** You are given a roof with rectangular base OABC where OA = 14 m along unit vector i, OC = 8 m along unit vector j, and the top edge DE is 6 m long and 5 m

Vector Hexagon

1. **Problem Statement:** Given vectors $\overrightarrow{AB} = 3p + q$ and $\overrightarrow{BC} = 4p$, and point $O$ inside a hexagon with vertices $A, B, C, D, E, F$, find the vec

Tam Giac Deu Vector

1. **Nêu bài toán:** Cho tam giác đều ABC, các điểm M, N, P sao cho $\overrightarrow{BM} = k \overrightarrow{BC}$, $\overrightarrow{CN} = \frac{2}{3} \overrightarrow{CA}$, \(\o

Position Vector X

1. **State the problem:** We have parallelogram OPQT with position vectors $ \overrightarrow{OP} = \mathbf{a} $ and $ \overrightarrow{OT} = \mathbf{b} $. Point K lies on PQ suc

Vector Ratio

1. Stating the problem: We have triangle OMN with vectors $\overrightarrow{OM} = a$ and $\overrightarrow{ON} = b$. Point R lies on MN such that $MR : RN = 3 : 2$. We need to prove

Tetrahedron Volume

1. **Problem Statement:** Find the volume of the tetrahedron determined by vectors $\mathbf{a} = 2\mathbf{i} - 3\mathbf{j} + \mathbf{k}$, $\mathbf{b} = \mathbf{i} + 2\mathbf{j} - \