Question

A farmer has to go 6 m due North, 8 m due Eastand 10 m due upwards to reach his fieldI.What is the displacement from his house to the field?​

Answer 1

Answer:-

For figure refer attachment.

Given:-

AB=6m.

BC=8m.

CD=10m.( vertically up).

Explanation:-

x component of displacement is 8m.

.y component of displacement is 6m

z component of displacement is 10m.

so, position vector becomes P(8,6,10).

Solving through vector analysis

Modulus of a vector ai + bj +ck is

given by √(a²+b²+c²)

Resultant displacement will be

${ac} = \sqrt{36+64+100}$

$ac = \sqrt{200}$

$ac =10 \sqrt{2}$

ac=10×1.414=14.14m.

Displacement of man from his home=

Displacement of man from his home=$ac =10 \sqrt{2}$ or 14.14 m.