Physics Motion in Plane

$H_{max}=\frac{u^{2}si{n}^2\theta }{2g}=\frac{{\left(25*sin45°\right)}^2}{2*10}=15.625m$

$T=\frac{usin\theta }{g}=\frac{25*sin45}{10}=1.77s$

First angle, θ₁= θ, $R=\frac{u^{2}sin2\theta }{g}$      

Another angle (θ₂ = 90 - θ) for which range will be Same as that of θ₁ =θ

$R^1=\frac{u^{2}sin2\left(90-\theta \right)}{g}=\frac{u^2}{g}sin2\theta =R$

at ${\theta }_1=\theta ,h_1=\frac{u^{2}si{n}^2\theta }{2g}$

$\&{\theta }_2=90-\theta ,h_2=\frac{u^{2}si{n}^2{\theta }_2}{2g}=\frac{u^{2}co{s}^2\theta }{2g}$

$\Rightarrow h_1{h}_2=\frac{1}{4^2}{\left[\frac{u^{2}sin2\theta }{g}\right]}^2$

$h_1{h}_2=\frac{1}{4^2}{R}^2$

$R=4\sqrt[]{h_1{h}_2}$

So, Both statement is true & Reason is correct explanation for statement 1.

Mass and temperature are scalars. We can fully describe them by magnitude alone and do not involve direction. 

Speed is a scalar quantity. It only has magnitude and no direction, unlike velocity, which is a vector.

Displacement, velocity, and acceleration are common vectors. These three vectors they have both magnitude and direction, and  follow vector addition rules.

Graphically, we place vectors head-to-tail. Analytically, we add components along axes using coordinate geometry, trigonometric functions, and unit vectors for precise vector resultant calculation.

It resolves vectors into components, adds corresponding x and y values algebraically, then reconstructs the resultant using magnitude and direction. That is, applying vector addition rules.

Vector resolution is important when analysing motion in two or three dimensions. It's used in vector addition and subtraction, projectile motion, and expressing velocity or acceleration using component form. Resolution with unit vectors also helps in applying kinematic equations to multidimensional problems. 

Vectors can be resolved generally into any two non-parallel directions. These are done more as rectangular components using unit vectors. The latter is most common in physics and engineering to represent them into Cartesian coordinates for simplified vector operations.