State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful
Adding a scalar to a vector of dimensions

5

(a)

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful
Adding any two vectors

5

(a)

State the reason , whether the following algebraic operations with scalar and vector physical quantities are meaningful.
adding a component of a vector to the same vector.

5

(a)

If A and B are two vectors such that \(\left| A\times B \right| =\sqrt { 3 } A.B\) Then,
Also, find the value of  \(\left| A\times B \right| \)

5

(a)

A ball rolls of the top of a stairway with horizontal velocity of 1.8 m/s. The steps are 0.24 m high and 0.2 m wide. Which step will the ball hit first? Take g=9.8 m/s²

5

(a)

\(\hat { i } \) and \(\hat { j } \) are unit vectors along x- and y- axis respectively. What is the magnitude and direction of the vectors \(\hat { i } \)+\(\hat { j } \) , and \(\hat { i } \)-\(\hat { j } \) ? What are the components of a vector \(\overset\rightarrow{A}\) =2\(\hat { i } \)+3\(\hat { j } \)along the directions  \(\hat { i } \) + \(\hat { j } \) and  \(\hat { i } \) - \(\hat { j } \) ?   [You may use graphical method]

5

(a)

Mathematically describe the motion of a particle along a plane (or along a two-dimensional plane).

5

(a)

A particle is thrown over a triangle from one end of a horizontal base that grazing the vertex falls on the other end of the base. If \(\alpha\) and \(\beta\) be the base angles and \(\theta\) the angle of projection; prove that: tan \(\theta\) = tan \(\alpha\)+ tan\(\beta\)

5

(a)

Define angular velocity and angular acceleration. The total speed V₁of a projectile at its greatest height is \(\sqrt{6\over7}\) of its speed V₂ when it is at half its greatest height. Show that the angle of projection is 30°.

5

(a)

If the horizontal range of projectile be a and the maximum height attained by it is b, then prove that the velocity of projectile is \([2g({b+{a^2\over 16b}})]^{1/2}\)

5

(a)