9000100709
Level:
B
Find the value of the parameter \(z\)
so that the vector \(\vec{w} = (8;2;z)\)
is perpendicular to the vectors \(\vec{a} = (1;2;-3)\)
and \(\vec{b} = (-1;2;1)\).
\(z = 4\)
\(z = -12\)
\(z = 2\)
\(z = -4\)
Points and Vectors
9000100710
Level:
A
Given points \(A = [-3;2]\) and
\(B = [1;y]\), find the values of
\(y\) which ensure the
length of the vector \(\overrightarrow{AB } \)
equals \(5\).
\(y_{1} = -1\),
\(y_{2} = 5\)
\(y_{1} = -1\),
\(y_{2} = 1\)
\(y_{1} = 1\),
\(y_{2} = 5\)
\(y_{1} = 5\),
\(y_{2} = -5\)
9000100706
Level:
B
Given vectors \(\vec{a} = (-1;2;-3)\),
\(\vec{b} = (0;1;-1)\), find the
vector \(\vec{c}\)
perpendicular to both of them.
\(\vec{c} = (-1;1;1)\)
\(\vec{c} = (-3;0;1)\)
\(\vec{c} = (2;4;2)\)
\(\vec{c} = (-1;-1;1)\)
9000101803
Level:
A
In the following list identify a pair of points
\(C\),
\(D\) such that the
vector \(\overrightarrow{CD } \) is not
equal to the vector \(\overrightarrow{AB } \)
where \(A = [1;3;-2]\)
and \(B = [-2;4;3]\).
\(C = [1;-2;3],\ D = [-2;-1;-2]\)
\(C = [6;1;-4],\ D = [3;2;1]\)
\(C = [-3;5;7],\ D = [-6;6;12]\)
\(C = [-3;8;14],\ D = [-6;9;19]\)
9000100704
Level:
A
Given vectors \(\vec{a} = (2;2;-3)\),
\(\vec{b} = (-1;0;1)\),
\(\vec{c} = (0;-2;1)\), find the length
of the vector \(\vec{u} =\vec{ a} - 2\vec{b} + 3\vec{c}\).
\(|\vec{u}| = 6\)
\(|\vec{u}| = 5\)
\(|\vec{u}| = 4\)
\(|\vec{u}| = 3\)
9000101802
Level:
B
Among vectors \(\vec{u} = \left (- \frac{2}
{\sqrt{2}};2\sqrt{2}\right )\),
\(\vec{v} = (-5;10)\),
\(\vec{w} = (2.5;-5)\),
\(\vec{r} = (-3.5;6)\)
find the vector which is not parallel to the vector
\(\vec{a} = (1;-2)\).
\(\vec{r}\)
\(\vec{w}\)
\(\vec{v}\)
\(\vec{u}\)
9000100707
Level:
B
Consider points \(A = [-2;-1]\),
\(B = [1;y]\),
\(C = [3;-4]\). Find the coordinate
\(y\) which ensures
that the vectors \(\overrightarrow{AB } \)
and \(\overrightarrow{AC } \)
are perpendicular.
\(y = 4\)
\(y = -4\)
\(y = 0.8\)
\(y = -0.8\)
9000100708
Level:
B
Given points \(A = [-2;-1]\),
\(B = [x;-3]\),
\(C = [4;-4]\), find the coordinate
\(x\) which ensures
that the vectors \(\overrightarrow{AB } \)
and \(\overrightarrow{AC } \)
are parallel.
\(x = 2\)
\(x = 7\)
\(x = -3\)
\(x = 3\)
9000101801
Level:
A
Among vectors \(\vec{a} = (-1;2;0)\),
\(\vec{b} = (2;1;2)\),
\(\vec{c} = (1;3;0)\) and
\(\vec{d} = (-3;0;0)\) find a
pair of vectors with equal length.
\(\vec{b}\),
\(\vec{d}\)
\(\vec{a}\),
\(\vec{c}\)
\(\vec{a}\),
\(\vec{d}\)
\(\vec{b}\),
\(\vec{c}\)
9000100701
Level:
A
Given vectors \(\vec{a}\),
\(\vec{b}\),
\(\vec{c}\),
\(\vec{d}\), find
\(\vec{a} +\vec{ b} +\vec{ c} +\vec{ d}\).
\((-1;-2)\)
\((17;7)\)
\((6;10)\)
\((2;-3)\)