Question

A particle goes from x1 = -2m, y1 = 3m, z1 = 1m to x2= 3m, y2= 2m and z2 = 4m. What is its displacement vector (in m)?

Answer 1

Answer:

5m in x direction

1 m in y direction

3 m in -ve z direction

Explanation:

x1 = -2m, y1 = 3m, z1 = 1m can be written as

(-2 i + 3j + 1k) say A

and x2= 3m, y2= 2m and z2 = 4m can be written as

(3i + 2j + 4k) say B

so displacement vector = B - A

=3i -(-2i) + 3j - 2j + 1k - 4k

= 5i + j - 3k

5m in x direction

1 m in y direction

3 m in -ve z direction

hope it helps :)

Answer 2

Answer:

5i + j - 3k

Explanation:

Given: $x_1$ = -2m, $y_1$ = 3m, $z_1$ = 1m and $x_2$= 3m, $y_2$= 2m and $z_2$ = 4m.

To find: Displacement vector

Solution: Position Vector: The position of an object in relation to the origin is represented by its position vector at time t. A straight line connecting the origin and the place at time t is used to depict it. An essential mathematical notion is a displacement vector. A vector, that is. It shows the direction and length of a straight line travelled by an object. In physics, the phrase "displacement vector" is frequently used to describe the speed, acceleration, and distance that an item travels with respect to a fixed point or its initial position.

From the question particle direction can be framed as :

A= -2 i + 3j + 1k

B= 3i + 2j + 4k

Now the displacement vector can be calculated as:

Displacement vector = B-A

=3i -(-2i) + 3j - 2j + 1k - 4k

= 5i + j - 3k

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