Area of parallelogram
Compute the area of the parallelogram in the cartesian space whose 4 vertices are ($val14,$val15,$val16) , ($val17,$val18,$val19) , ($val20,$val21,$val22) , ($val23,$val24,$val25) .
Area of triangle
Compute the area of the triangle in the cartesian space whose 3 vertices are ($val14,$val15,$val16) , ($val17,$val18,$val19) , ($val20,$val21,$val22) .
Angle
We have 3 points in the space:
,
,
.
Compute the angle
(in degrees, between 0 and 180).
Combination
Let
,
,
be three space vectors. Compute the vector
.
Combination 2 vectors
Let
,
be three space vectors. Compute the vector
.
Combination 4 vectors
Let
,
,
,
be four space vectors. Compute the vector
.
Find combination
Let
,
,
be three space vectors. Try to express
as a linear combination of v1,
and
:
.
Find combination 2 vectors
Let
,
,
be two space vectors. Try to express
as a linear combination of
and
:
.
Given scalar products
Let
,
,
be three space vectors. Find the vector
having the following scalar products:
,
,
.
Given vector product
Let
be a space vector. Determine the vector
such that the vector product
equals ($val14,$val15,$val16).
Vector product and length
Let
be a space vector. We have another vector v which is perpendicular to
. Given that the length of
is equal to $val11, what is the length of the vector product
?
Vector product and length II
Let
be a space vector. We have another vector
whose length is $val10. Given that the scalar product
, what is the length of the vector product
?
Vertex of parallelogram
We have a parallelogram
in the cartesian space, whose 3 first vertices are at the coordinates
= ($val14,$val15,$val16) ,
= ($val17,$val18,$val19) ,
= ($val23,$val24,$val25) .
Compute the coordinates of the fourth vertex
.
Perpendicular to two vectors
Let
,
be two space vectors. We have a vector
which is perpendicular to both
and
. What is this vector
?
Perpendicular and vector product
Let
be a space vector. Find the vector
who is perpendicular to
, such that the vector product u
is equal to ($val25,$val26,$val27).
Linear relation
We have 4 space vectors:
,
,
,
.
Find 4 integers
,
,
,
such that
,
but the integers
,
,
,
are not all zero.
Scalar and vector products
Let
be a space vector. Find the vector
such that the scalar product and the vector product
,
.
Volume of parallelepiped
Compute the volume of the parallelepiped in the cartesian space having a vertex
, and such that the 3 vertices adjacent to
are
= ($val20,$val21,$val22) ,
= ($val23,$val24,$val25) ,
= ($val26,$val27,$val28) .
Volume of tetrahedron
Compute the volume of the tegrahedron in the cartesian space whose 4 vertices are
= ($val17,$val18,$val19) ,
= ($val20,$val21,$val22) ,
= ($val23,$val24,$val25) ,
= ($val26,$val27,$val28) .