Points and Vectors
Dot Product of Vectors
2010015707
Level:
A
Given vectors \(\vec{a} = (-1;2;1)\),
\(\vec{b} = (0;-1;1)\), and
\(\vec{c} = (-2;0;1)\), find the length
of the vector \(\vec{u} =\vec{ a} - 2\vec{b} + \vec{c}\).
\(|\vec{u}| = 5\)
\(|\vec{u}| = \sqrt{10}\)
\(|\vec{u}| = 3\)
\(|\vec{u}| = 1\)
2010015706
Level:
A
Given the vectors \(\vec{a}\),
\(\vec{b}\), and
\(\vec{c}\), find
\(\vec{a} - 3\vec{b} +\vec{ c}\).
\((10;5)\)
\((-8;5)\)
\((-8;-1)\)
\((7;5)\)
2010015705
Level:
A
We are given points \( A = [2;1] \), \( B = [7;2] \), and \( T = [4;3] \), where point \( T \) is the centroid of triangle \( ABC \). Find the coordinates of \( C \), which is the vertex of \( ABC \).
\( C = [3;6] \)
\( C = [4;8] \)
\( C = [3.5;7] \)
\( C = [5;6] \)