Chapter 2: Main Application
82
Syntax 4: You can solve for the relationship between two points, straight lines, planes, or spheres by entering
a vector equation inside the solve( command. Here we will present four typical syntaxes for solving
a vector equation using the solve( command.
In the syntaxes below, Vct-1 through Vct-6 are column vectors with three (or two) elements, and
s
,
t
,
u
and
v
are parameters.
solve(Vct-1 +
s
* Vct-2 [= Vct-3, {variable-1}])
• If the right side of the equation (= Vct-3) is omitted in the above syntax, it is assumed that all of the
elements on the right side are 0 vectors.
solve(Vct-1 +
s
* Vct-2 = Vct-3 +
t
* Vct-4, {variable-1, variable-2})
solve(Vct-1 +
s
* Vct-2 +
t
* Vct-3 = Vct-4 –
u
* Vct-5, {variable-1, variable-2, variable-3})
solve(Vct-1 +
s
* Vct-2 +
t
* Vct-3 = Vct-4 –
u
* Vct-5 +
v
* Vct-6, {variable-1, variable-2, variable-3,
variable-4})
• Variables (variable 1 through variable 4) can be input into the
elements of each vector (Vct-1 through Vct-6) in the above four
syntaxes to solve for those variables.
0234
To prove whether point P (5, 7, 9) and point Q (5, 7, 8) each exist on straight line
l
, which is an
orientation vector (4, 5, 6) that passes through point A (1, 2, 3)
Note
For the solution, the solve function returns an expression or value for the expression (Exp/Eq) input as its
argument. The message “More solutions may exist” will appear on the display when a value is returned as the
solution, because there may be multiple solutions.
The solve function can return a maximum of 10 solutions in the case of values.
Example: To solve cos (
x
) = 0.5 for
x
(initial value: 0)
(Angle unit setting: Deg)
u
dSolve
[Action][Equation/Inequality][dSolve]
Function: Solves first, second or third order ordinary differential equations, or a system of first order
differential equations.
Syntax: dSolve(Eq, independent variable, dependent variable [, initial condition-1, initial condition-2][, initial
condition-3, initial condition-4][, initial condition-5, initial condition-6] [ ) ]
dSolve({Eq-1, Eq-2}, independent variable, {dependent variable-1, dependent variable-2} [, initial
condition-1, initial condition-2, initial condition-3, initial condition-4] [ ) ]
• If you omit the initial conditions, the solution will include arbitrary constants.
• Input all initial conditions equations using the syntax Var = Exp. Any initial condition that uses any other
syntax will be ignored.
Example: To solve a differential equation
y
’ =
x
, where
y
= 1 when
x
= 0
Example: To solve the system of first order differential equations
y
’ =
y
+
z
,
z
’ =
y
–
z
, where “
x
” is the
independent variable, “
y
” and “
z
” are the dependent variables, and the initial conditions are
y
= 3
when
x
= 0, and
z
=
'
2 – 3 when
x
= 0
