For two vectors A and B, |A + B|= |A – B| is always true when
A. |A| |B| ≠ 0
B. A ⊥ B
C. |A| = |B| ≠ 0 and A and B are parallel or anti parallel
D. When either |A| or |B| is zero
It is given that , it could be true when |A|=0 or |B|=0 or both are zero.
The given statement can also be true if both conditions are applied together that is
Therefore we can write,
This gives the always true condition that is when A is perpendicular to B.
Rate this question :
Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in Cartesian co-ordinates A = Axî + Ayĵ where î and ĵ are unit vector along x and y directions, respectively and Ax and Ay are corresponding components of (Fig. 4.9). Motion can also be studied by expressing vectors in circular polar co-ordinates as A = Ar + Aɵ where = = cosθ î + sin θ ĵ and = − sin θ î +cos θ ĵ are unit vectors along direction in which ‘r’ and ‘θ ’ are increasing.
(a) Express î and ĵ in terms of and .
(b) Show that both ř and θ are unit vectors and are perpendicular to each other.
(c) Show that (ř) = ω where and = −ωř
(d) For a particle moving along a spiral given by r= aθ , where a = 1 (unit), find dimensions of ‘a’.
(e) Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.
Physics - Exemplar
A man wants to reach from A to the opposite corner of the square C (Fig. 4.10). The sides of the square are 100 m. A central square of 50m × 50m is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of v m/s (v < 1). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?
Physics - Exemplar
If |A|= 2 and |B| = 4, then match the relations in column I with the angle θ between A and B in column II
If |A| = 2 and |B| = 4, then match the relations in column I with the angle θ between A B and in column II.
A, B and C are three non-collinear, non-co-planar vectors. What can you say about direction of A × (B × C)?Physics - Exemplar
Consider the quantities, pressure, power, energy, impulse, gravitational potential, electrical charge, temperature, area. Out of these, the only vector quantities arePhysics - Exemplar