Vector Equations,algebra Revision Notes From A-level Maths Tutor
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Pure Maths
Vectors A-level Maths Tutor
www.a-levelmathstutor.com
topic notes [email protected]
Vectors : Vector Equations
Component rules Consider two vectors: a = x1 i +
y1 j + z1 k
and
b = x2 i +
y2 j + z2 k
in three dimensional space.
a = b implies that a+b = a-b
=
x1 = x2
y1 = y2
z1 = z2
( x1+ x2 )i
+
( y1+ y2 )j
+
( z1+ z2)k
( x1- x2 )i
+
( y1- y2 )j
+
( z1- z2)k
ma = mx1i + m y1j + mz1k
where m is a scalar quantity
in 3D space, if point A has position vector a and point B has position vector b then the distance AB is given by:
A-level Maths Tutor
www.a-levelmathstutor.com
[email protected]
Vectors A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
topic notes [email protected]
Equation straight line - single point & parallel vector given
A(x1
y1 z1) is a fixed point on the line
a is the position vector for point A
a=
x1i + y1 j+ z1k
s is a vector parallel to the line s = l i + m j+ n k ( l m n are called the direction ratios of the line)
r is the position vector for an arbitrary point P(x,
A-level Maths Tutor
y, z) on the line.
www.a-levelmathstutor.com
[email protected]
Vectors A-level Maths Tutor
A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
www.a-levelmathstutor.com
topic notes [email protected]
[email protected]
Vectors A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
topic notes [email protected]
Equation of a straight line - two points given
A(x1
y1 z1) is a fixed point on the line
a is the position vector for point A
B(x2
a=
x1i + y1 j+ z1k
y2 z2) is a fixed point on the line
b is the position vector for point B
b=
x2i + y2 j+ z2k
r is the position vector for an arbitrary point P(x,
A-level Maths Tutor
y, z) on the line.
www.a-levelmathstutor.com
[email protected]
Vectors A-level Maths Tutor
A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
www.a-levelmathstutor.com
topic notes [email protected]
[email protected]
Vectors A-level Maths Tutor
www.a-levelmathstutor.com
topic notes [email protected]
Vectors : Vector Equations
Component rules Consider two vectors: a = x1 i +
y1 j + z1 k
and
b = x2 i +
y2 j + z2 k
in three dimensional space.
a = b implies that a+b = a-b
=
x1 = x2
y1 = y2
z1 = z2
( x1+ x2 )i
+
( y1+ y2 )j
+
( z1+ z2)k
( x1- x2 )i
+
( y1- y2 )j
+
( z1- z2)k
ma = mx1i + m y1j + mz1k
where m is a scalar quantity
in 3D space, if point A has position vector a and point B has position vector b then the distance AB is given by:
A-level Maths Tutor
www.a-levelmathstutor.com
[email protected]
Vectors A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
topic notes [email protected]
Equation straight line - single point & parallel vector given
A(x1
y1 z1) is a fixed point on the line
a is the position vector for point A
a=
x1i + y1 j+ z1k
s is a vector parallel to the line s = l i + m j+ n k ( l m n are called the direction ratios of the line)
r is the position vector for an arbitrary point P(x,
A-level Maths Tutor
y, z) on the line.
www.a-levelmathstutor.com
[email protected]
Vectors A-level Maths Tutor
A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
www.a-levelmathstutor.com
topic notes [email protected]
[email protected]
Vectors A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
topic notes [email protected]
Equation of a straight line - two points given
A(x1
y1 z1) is a fixed point on the line
a is the position vector for point A
B(x2
a=
x1i + y1 j+ z1k
y2 z2) is a fixed point on the line
b is the position vector for point B
b=
x2i + y2 j+ z2k
r is the position vector for an arbitrary point P(x,
A-level Maths Tutor
y, z) on the line.
www.a-levelmathstutor.com
[email protected]
Vectors A-level Maths Tutor
A-level Maths Tutor
Pure Maths www.a-levelmathstutor.com
www.a-levelmathstutor.com
topic notes [email protected]
[email protected]
