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Respected sir, How to know when to use scalar product i.e. dot between two vectors and vector product i.e cross between two vectors while solving the application based questions ? While finding the perpendicular of a parallelogram given the area we use vector product for vectors for finding area, but why and how will we know when to use what?

Respected sir,
How to know when to use scalar product i.e. dot  between two vectors and vector product i.e cross between two vectors while solving the application based questions ? While finding the perpendicular of a parallelogram given the area we use vector product for vectors for finding area, but why and how will we know when to use what?

Grade:11

1 Answers

Rajdeep
231 Points
5 years ago
Hello there!
 
According to me, there is no such rule to identify when to use what (scalar product or vector product).
 
You need to understand the question and the approach to solve the question.
 
If in the question, it is stated that the vectors A and B are perpendicular,
use dot product = 0, as dot product of \small A.B = ABcos\Theta, and cos 90 = 0.
 
If in the question, it is stated that the vectors A and B are parallel,
use cross product = 0, as cross product of \small A\times B = ABsin\Theta, and sin 0 = 0.
 
If two vectors A and B represent the two adjacent sides of a parallelogram,
then the area of the parallelogram is the cross product (or vector product) of the two vectors.
 
If two vectors A and B represent the two sides of a triangle,
then the area of the triangle is half the cross product of the two vectors.
 
 

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