VECTOR:

A vector is nothing but the one which has magnitude and direction.

COLLINEAR VECTOR:

Two vectors ai+bj and ci+dj are said to be parallel when a=c and b=d.

COPLANAR VECTORS:

Vectors are said to be coplanar when the y are in the same plane.

ADDITION OF VECTORS:

Two vectors can be added using parallelogram rule and triangle rule.But using triangle rule we can solve most of the equations.If two vectors a and b are inclined through an angle q then the resultant of two vectors

is (a^2+b^2+2abcosq)^(1/2) here q is the included angle between a and b.

SUBTRACTION OF VECTORS:

Subtraction of two vectors is nothing but the addition of two vectors the difference is only we are adding another vector with a negative sign

SCALAR MULTIPLICATION:

A vector can be multiplied with a scalar when multiplied with a scalar the magnitude will only be changed.Direction of vector remains unchanged.

A scalar multiplication follows commutative rule and assosciative rule and distributive rule.

ANGLE BETWEEN TWO VECTORS:

Angle between two vectors can be found using the dot product and vector product.

DOT PRODUCT:

If a and b are two vectors and q is the included angle between the vectors then cosq=a.b/|a|*|b|.If two vectors are perpendicular then dot product is zero.

VECTOR PRODUCT:

If a and b are two vectors and q is the included angle between the vectors then the vector product is defined as sinq=a*b/|a|8|b|.If two vectors are parallel then vector product is zero.

LINEAR COMBINATION OF TWO VECTORS:

Any vector can be expressed as a sum of two or more vectors.

LINEAR DEPENDENT AND LINEAR INDEPENDENT VECTORS:

Vectors are said to be linearly dependent when a vector is expressed as a sum of of other vectors and linear independent is the reverse of the above statement.

DIRECTIONAL COSINES:

When a vector is place in a three dimensional space it will be making three angles with x y z axes.Let h j k are the angles made by the vector with the three axes then cosh=x component of the vector/magnitude of the vector.

cosj=y component of the vector/magnitude of the vector.

cosk=z component of the vector/ magnitude of the vector.

MAGNITUDE OF THE VECTOR:

Let the vector a=bi+cj+dk then the magnitude of this vector is defined as|a|=(d^2+b^2+c^2)^(1/2).

TRIPLE PRODUCT OF VECTORS:

A vector is nothing but the one which has magnitude and direction.

COLLINEAR VECTOR:

Two vectors ai+bj and ci+dj are said to be parallel when a=c and b=d.

COPLANAR VECTORS:

Vectors are said to be coplanar when the y are in the same plane.

ADDITION OF VECTORS:

Two vectors can be added using parallelogram rule and triangle rule.But using triangle rule we can solve most of the equations.If two vectors a and b are inclined through an angle q then the resultant of two vectors

is (a^2+b^2+2abcosq)^(1/2) here q is the included angle between a and b.

SUBTRACTION OF VECTORS:

Subtraction of two vectors is nothing but the addition of two vectors the difference is only we are adding another vector with a negative sign

SCALAR MULTIPLICATION:

A vector can be multiplied with a scalar when multiplied with a scalar the magnitude will only be changed.Direction of vector remains unchanged.

A scalar multiplication follows commutative rule and assosciative rule and distributive rule.

ANGLE BETWEEN TWO VECTORS:

Angle between two vectors can be found using the dot product and vector product.

DOT PRODUCT:

If a and b are two vectors and q is the included angle between the vectors then cosq=a.b/|a|*|b|.If two vectors are perpendicular then dot product is zero.

VECTOR PRODUCT:

If a and b are two vectors and q is the included angle between the vectors then the vector product is defined as sinq=a*b/|a|8|b|.If two vectors are parallel then vector product is zero.

LINEAR COMBINATION OF TWO VECTORS:

Any vector can be expressed as a sum of two or more vectors.

LINEAR DEPENDENT AND LINEAR INDEPENDENT VECTORS:

Vectors are said to be linearly dependent when a vector is expressed as a sum of of other vectors and linear independent is the reverse of the above statement.

DIRECTIONAL COSINES:

When a vector is place in a three dimensional space it will be making three angles with x y z axes.Let h j k are the angles made by the vector with the three axes then cosh=x component of the vector/magnitude of the vector.

cosj=y component of the vector/magnitude of the vector.

cosk=z component of the vector/ magnitude of the vector.

MAGNITUDE OF THE VECTOR:

Let the vector a=bi+cj+dk then the magnitude of this vector is defined as|a|=(d^2+b^2+c^2)^(1/2).

TRIPLE PRODUCT OF VECTORS:

If there are three vectors a b c then a*(b*c)=(a.b)c-(c.a)*b.

As in case of dot product commutative holds good where as in case of vector product commutative does not holds good.

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