You can only unlock the chapter using a special code that we will send you via the Viber app. Receiving a message is free of charge and with no obligations.
My phone number:
Get a code
In compliance with the law, persons under the age of 15 can enter their phone number only in the presence of a parent or guardian.
4-character code:
Check the received code
The page will be refreshed automatically in a few seconds.
To ensure the proper functioning of the website, OpenProf uses cookies that do not store personal data. By continuing to use the website, you agree to cookies. Tell me more »
and 
express the following vectors:
and 
express vectors:
and 
as illustrated in the image below, in component vectors 
and 
.
and 
express vectors:
and 
express vectors:
and 
express vectors:
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 
. For which real number 
are the vectors 
and 
rectangular? For which real numbers 
is the length of the vector 
equal to 7?
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 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 
.
and 
are given, for which 
, 
apply, and the angle between the vectors is the same as 
.
and 
.
and 
are given. Express the vectors 
and 
with the given vectors 
and 
. Calculate the angle between the vectors 
and 
are given, for which 
, 
apply, and the angle between the vectors is equal to 
. Calculate the angle between the vectors 
.
and 
is given.
, 
, 
and 
with the given vectors.
collinear?
.
and 
.
, 
and 
are equal to 5. The vectors 
and 
if:
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 
is 10, the length of the vector 
6, and the length of the vector 
is 18. Calculate the length of the vector 
.
, point P divide the line CD in the ratio 
. Using the vectors 
and 
express the vector 
and calculate 
.
, 
cm and 
.
, 
and 
.
m, 
m and as 
are given. Calculate the lengths of both diagonals.
, 
and 
.
and 
with the given vectors 
and 
. Calculate the scalar product 
.
cm, 
cm and 
.
cm, 
cm and 
cm, as 
is a point S the midpoint of the side EH. Calculate the size of the angle 
.
and 
long. The point T should lie on the line AD so that 
. Let 
and 
.
, 
and 
. Express the vector 
. Prove that the vectors 
are perpendicular.
and express the vector 
.
. The traction force of the armor with the ground is at an angle of 30°. How much work do we do on the 
route?
draw a regular hexagon ABCDEF. Draw the vector 
and calculate its length.
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 
.
is equal to 3, calculate the values of x and y.
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 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.
. Write the vectors 
and 
as a linear combination of the vectors 
and 
. Calculate the exact length of the vector 
.
, 
and 
, draw the vectors 
and 
. Write the vectors 
and 
with coordinates (components) and calculate the scalar product 
.
between the vectors 
and 
and the vector 
;
with the components.
and 
:
are given. For which scalar value m is the vector mv the local vector of the point on the line p?
holds if the components of the vectors are 
and 
.
and 
write the vector 
as a combination of 
and 
.
and 
lie in the same plane?
and 
are given. Are the given vectors parallel?
and 
express vector 
as a linear combination.
and 
are given express vector 
as a linear combination.
and 
are given. Calculate the vector 
and, without using a computer, check that the given vector is: 
.
