Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.
Yes, if the angle between the two vectors is more than 90o but less than 2700. (cosΘ is negative)
It is theoretically possible for a substance to have a negative value of cubical expansivity, which means that the substance would contract rather than expand when the temperature increases. However, it is very rare for a substance to have a negative value of cubical expansivity over a significant range of temperatures.
One example of a substance that has a negative value of cubical expansivity over a limited range of temperatures is water. Water has a positive value of cubical expansivity at...
Log2aa=x then, a=(2a)x ......(1)
Log3a2a=y then,2a=(3a)y ......(2)
Log4a 3a=z then, 3a=(4a)z ......(3)
So,
a=(2a)x [from (1)]
Or, a=(3a)xy [from(2)]
Or, a=(4a)xyz [from(3)]
Multiplying both sides by 4a,
4a.a=4a.(4a)xyz
Or,(2a)² =(4a)xyz + 1
Or,(3a)2y =(4a)xyz+1
Or,(4a)2yz =(4a)xyz+1
Or, 2yz = xyz+1 .proved.


