OEF Vectors 3D --- Introduction ---

This module contains actually 19 exercises on vectors in 3D (linear combinations, angle, length, scalar product, vector product, cross product, etc.).

Area of parallelogram

Compute the area of the parallelogram in the cartesian space whose 4 vertices are
(,,) , (,,) , (,,) , (,,) .

Area of triangle

Compute the area of the triangle in the cartesian space whose 3 vertices are
(,,) , (,,) , (,,) .

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 (,,).

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 , 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 . 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
= (,,) , = (,,) , = (,,) .
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 (,,).

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
= (,,) , = (,,) , = (,,) .

Volume of tetrahedron

Compute the volume of the tegrahedron in the cartesian space whose 4 vertices are
= (,,) , = (,,) , = (,,) , = (,,) .

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• Description: collection of exercises on 3D vectors. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games
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