But cant the direction be opposite with the magnitude 1????

180 +  and - can also solve the purpose

Maybe my answer is wrong

but still i will try, if um wrong do tell me

 

I think the answer is c) more than 2 values of

2u X 3v = 6 u.v Sin  = 6 sin           ( since u and v are unit vectors)

for the above product to be unit vector it its magnitude should be 1

taking a constant direction, its magnitude must be 1 or -1

since sin has 4 values( 2 for 1/6 and 2 for -1/6) in one period hence possible values of  are 4 ie more than 2

The Charge Produced in Sky has a Sort of Potential Energy associated with it.

When The charges Displace in form of a thunder. There's a Conversion of PE into Other forms like Heat, Light and Sound Energy. Its just simple

Let the nos. be x and y

1st condition. x + y = (1/2)

 => x= (1/2) - y                             -(1)

 

To find:

minima for x + y³

from (1) f(y) = (1/2) - y + y³

f'(y) = -1 + 3y² = 0  (COnd. for Max/ MIN)

=> y = (1/^{[ ]}3)

f''(y) = 6y 

By 2nd derivative test  f''(y) >0 ie y= (1/root3)

 

Hence x = (1/2) - y

= (root3 - 1)/ 2root3

This Question can be solved by Simply comparing areas os the Independent triangles

 

Let ABC be an equilateral triangle and P be any point in the interior of it.

Let  Pl , Pm and Pn perpendicular to the sides AB , BC and CA.

 

Now area of Triangle ABC = ^{[ ](}3)/4 a²  = 25^{[ ]}3

Now ar triangle PAB = 1/2 * base * ht

=10

and ar triangle PBC = 15

 

Therefore ar Triangle PAC = 25(^{[ ]}3 - 1)

Hence 1/2 * 10 * Pn = 25(^{[ ]}3 - 1)

hence Pn = 5(^{[ ]}3 - 1)

hence my answer is 5(^{[ ]}3 - 1)

 

 

Plzzzz Rate me. um new in this field

^{[ ]}(-1/3) can be written ^{[ ]}(-1) * 1/3 *^{[ ]}(3) so it becomes (1/3)i *^{[ ]}3