Question

Show that the magnitude of the cross product of two vectors is equal to the 2*area of triangle formed by the two vector

Answer 1

The cross product of two vector represent the area of the parallelogram formed by them . Now consider a parallelogram OKLM . whose adjecent sides OK and OM as shown in fig

As we know that

Area of parallelogram = base × height …………(1)

So in the figure base = OK = A ( VECTOR )

Height = Bsin ¥

So putting the value in equation (1) we get

Area of parallelogram = AB sin¥ = A× B = cross product of two vector A and B

I try to explain you in easiest method

My figure is not much good but you can understand ( smiling )

912 Views · View Upvoters · Answer requested by Aditi Kachhawaha

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Faizan Ahmed

Vivek

Vivek

Answered Sep 20, 2017

A2A

Because are of a parallelogram is given by ABsinθ

Where A and B are two sides of parallelogram and θ being the angle between them

But, |A⃗ ×B⃗ |=|A||B||sinθ|

Hope you got the point

VM

Answer 2

Step-by-step explanation:

Area of a parallelogram.

area of a parallelogram = Base × height.

= |A| × |B| sin Q

= |A| |B| sin Q

Area of a parallelogram =|A×B|

Hope you understood.

thank you!