Prove that axb (Vector cross product) is perpendicular to both a and b vector

 Prove that axb (Vector cross product) is perpendicular to both a and b vector if :- 

a vector = i + j - 3k

b vector = -i+2j-3k 

Ans:- 

Here, this question says that we should prove the question through vector process and find out the a vector and b vector is perpendicular to cross product of a vector and b vector . 

So in this question we should solve the problem by using the vector product rule. 

If there there is perpendicular situation then the dot product of two vector is zero. 

           i.e (axb).a=0 -------------------------(I)

As similar to the b vector 

           (axb).b=0 -----------------------(ii) 

So here to find answer first we must find the vector product of a and b in order to find the final result as per the question had asked. 

So, axb = |a||b|sin( theta) 

But here the value of a vector and b vector is given, so we can directly do the product by matrix method which is clearly given in this img solution : 

Now when we came to know vector product of axb then let's dot product is with a and b respectly. 

Here we have given the dot product to a only, you must do dot product with b too. But the answer will be 0 in both condition.

Hence (axb) perpendicular to a vector 

        And (axb) perpendicular to b vector 

-(((((((((((((((((((((((((((((((((((

This question may asked multiple choice questions or even in a conceptual answer questions in the exam.

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