Level:
Project ID:
1103030705
Accepted:
1
Clonable:
0
Easy:
0
Let there be a triangle KLM and vectors \( \overrightarrow{a} \), \( \overrightarrow{c} \) in the coordinate system. Triangle \( KLM \) and vectors \( \overrightarrow{a} \), \( \overrightarrow{c} \) are
given in the coordinate system shown in the picture. Point T is the centroid of the triangle KLM. Express vector \( \overrightarrow{x} \), where \( \overrightarrow{x}=\overrightarrow{KT} \) as a linear combination of \( \overrightarrow{a} \) and \( \overrightarrow{c} \) and evaluate \( \left|\overrightarrow{x}\right| \).
\( \overrightarrow{x}=\frac13 \overrightarrow{a}+\frac13 \overrightarrow{c} \), \( \left|\overrightarrow{x}\right|=5 \)
\( \overrightarrow{x}=\frac23 \overrightarrow{a}+\frac23 \overrightarrow{c} \), \( \left|\overrightarrow{x}\right|=10 \)
\( \overrightarrow{x}=\frac12 \overrightarrow{a}+\frac12 \overrightarrow{c} \), \( \left|\overrightarrow{x}\right|=\frac{15}2 \)
\( \overrightarrow{x}=\frac14 \overrightarrow{a}+\frac14 \overrightarrow{c} \), \( \left|\overrightarrow{x}\right|=\frac{225}{12} \)