Dot Product of Vectors
Points and 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 \( ABC \).
\( C = [3,6] \)
\( C = [4,8] \)
\( C = [3.5,7] \)
\( C = [5,6] \)
2010015704
Level:
A
Given the vectors \( \vec{a} \), \( \vec{b} \), and \( \vec{c} \) shown in the picture, express the vector \( \vec{c} \) as a linear combination of vectors \( \vec{a} \) and \( \vec{b} \).
\( \vec{c} = -\vec{a}-2\vec{b} \)
\( \vec{c} = -\vec{a} + \frac12 \vec{b} \)
\( \vec{c} = -2\vec{a} - \vec{b} \)
\( \vec{c} = 2\vec{a} + \frac32 \vec{b} \)