Note: Vector triple product is not in our Physics syllabus.

SCALAR OR DOT PRODUCT

Product of magnitude of two Vectors with cosine of angle between them.

For perpendicular Vectors: ,q = 90° and cos 90° = 0

Dot product of Standard unit Vectors:

are mutually perpendicular then

the value of m is

(a) - 2

(b) - 3

(c) + 3

(d) + 2

2 + m + 1 = 0

m = - 3                                                                                           Answer (b)

Method to find dot or Scalar product

Finding Scalar and Vector Component (projection)

Component (projection) in the direction and in the perpendicular direction

vector or cross product

Product of magnitude of two Vectors with sine of angle between them.

For perpendicular Vectors:

For parallel Vectors:

For antiparallel Vectors:

Cross or Vector product of Standard unit vectors

USING RIGHT HAND SCREW RULE

Method to find cross or vector product

AREA OF TRIANGLE

Area of parallelogram:

DIAGONAL OF PARALLELOGRAM

Example If the diagonals of a parallelogram are and  ,then area of this

parallogram will be

(a) 2 unit2                                        (b) 3 unit2

(c) 4 unit2                                        (d) 1 unit2

Example: Unit vector perpendicular to two vectors Finding a unit vector

perpendicular to

Example: Consider three Vectors

Scalar triple product

(a) 0

(b) 6

(c) 12

(d) 18

= 2 (3 n-2) -3 (15 + 1) -2 (10 + n) = 0

4n – 72 = 0