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and 
if 
.
for which 
?
the smallest? What is this minimum length?
and 
if their lengths are 
, 
, and the angle between the vectors is 
.
, 
and 
are given in the plane. Write down the components of the vectors 
and 
and calculate the angle, 
between them .
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
. Calculate the scalar product of the vectors and the length of the perpendicular projection of the vector 
and 
are drawn in the coordinate system. Draw the vector 
. What are the exact lengths of the vectors 
between 
and the vector 
are given.
with the components (coordinates).
and 
.
and 
. For which real number 
are the vectors 
and 
rectangular? For which real numbers 
is the length of the vector 
equal to 7?
and 
, and express the answer to the nearest degree and minute.
and 
if their lengths are 
, 
, and the angle between the vectors is 
.
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
. Calculate the scalar product of the vectors and the length of the perpendicular projection of the vector 
and 
. Calculate 
.
is given by 
.
.
if 
and 
.
, 
and 
are equal to 5. The vectors 
and 
if:
, 
and 
are given in space. Write down the components of the vectors 
and 
, then calculate the angle 
between them.
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
. Calculate the scalar product of the vectors and the length of the perpendicular projection of the vector 
are the vertices of the triangle;
.
is 6, the vectors 
and 
4, and the length of the vector 
is 5. The vectors lie in the plane as shown in the figure. Calculate the scalar product 
, 
and 
are given in space. We know that the point P bisects the line AB. Show that the vectors 
and 
are perpendicular.
and 
are given, for which 
, 
apply, and the angle between the vectors is the same as 
.
and 
.
and 
in surd form.
, point P divide the line CD in the ratio 
. Using the vectors 
and 
express the vector 
and calculate 
.
for which the vectors 
and 
are perpendicular.
and 
if their lengths are 
, 
, and the angle between the vectors is 
.
and 
are given. Express the vectors 
and 
with the given vectors 
and 
. Calculate the angle between the vectors 
and 
with the given vectors 
and 
. Calculate the scalar product 
.
so that the vectors 
and 
are inclined at an angle 
to each other.
, 
and 
are the vertices of triangle 
;
per minute.
of the side 
to two decimal places.
) of 
to two decimal places.
so that the quadrilateral 
is a parallelogram.
and 
.
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
. Calculate the angle between the vectors 
.
. Write the vectors 
and 
as a linear combination of the vectors 
and 
. Calculate the exact length of the vector 
.
and 
if their lengths are 
, 
, and the angle between the vectors is 
.
and 
is given.
, 
, 
and 
with the given vectors.
collinear?
.
and 
.
and 
are drawn in the coordinate system. Write these two vectors with components (coordinates). Calculate the vector 
and plot it in the coordinate system. Also calculate the vector 
.
and 
be vectors in the plane 
.
such that the vectors 
and 
are rectangular.
such that the vectors 
and 
parallel.
and 
so that they have a origin at the coordinate origin.
, write down its components and calculate its length.
and 
and the vector 
;
with the components.
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
. Draw the vector 
and calculate its length .
. In the trapezium is 
, 
and 
. Express the vectors with the vectors 
and 
:
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
.
and express the vector 
.
and 
define the parallelogram 
.
and 
. At what value of the x does the parallelogram become a rectangle?
. Point F bisects side CD, distances AE and BF intersect at point S. Calculate the ratio 
.
if 
, 
and 
. The angle between the vectors 
and 
measures 
.
the vectors 
, 
and 
.
and 
are orthogonal.
and the size of the angle 
between them. Round the size of the angle to two decimal places.
and 
are given.
and the bisector of the odd quadrants.
, 
and 
, draw the vectors 
and 
. Write the vectors 
and 
with coordinates (components) and calculate the scalar product 
.
between the vectors 
is 10, the length of the vector 
6, and the length of the vector 
is 18. Calculate the length of the vector 
.
