Question

A bird flies from (-3m, 4m. -3m) to (7m. -2m, -3m) in the xyz-coordinates. The bird's
displacement vector is given by :
(A) 49+27-66
(B) 10 - 61
(C) 4i-27
(D) 10 +63-6​

Answer 1

Answer:

Option (B) is correct.

Explanation:

Given:

Initial position of the bird = (-3m, 4m, -3m).

Final position of the bird = (7m, -2m, -3m).

In the unit vector notation,

The initial position vector of the bird with respect to origin is given by

$\vec r_1= (-3)\hat i + (4)\hat j +(-3)\hat k$.

The final position vector of the bird with respect to origin is given by

$\vec r_2= (7)\hat i + (-2)\hat j +(-3)\hat k$.

where,

$\hat i,\ \hat j,\ \hat k$ = unit vectors along x, y and z axes respectively.

The displacement vector is given by

$\vec r = \vec r_2 - \vec r_1\\=[(7)\hat i + (-2)\hat j +(-3)\hat k]-[(-3)\hat i + (4)\hat j +(-3)\hat k]\\=(7-(-3))\hat i +(-2-4)\hat j +(-3-(-3))\hat k\\=10\hat i +(-6)\hat k\\=10\hat i - 6\hat j.$

Thus, Option (B) is correct.