Question

A particle, initially at rest and having position vector (i + 7j – 8k)m in a coordinate system, starts moving with velocity (2i – j + k) m/s. The distance of the particle from the origin after 3 seconds from beginning of the motion in the same coordinatea system is :

• A. 10 m
• B. 10$\sqrt{2}$ m
• C. 3$\sqrt{10}$m
• D. 5$\sqrt{10}$ m

Answer 1

Answer: (C)

3$\sqrt{10}$m

Answer 2

∆$\overrightarrow{r}$ = $\overrightarrow{V}$t

= 6i – 3j + 3k

The position vector $\overrightarrow{R}$ of the particle after three second

$\overrightarrow{R}$ = $\overrightarrow{r}$₁ + $\overrightarrow{V}$t

= (i + 7j – 8k) + (6i – 3j + 3k) = 7i + 4j – 5k.

Distance from the origin.

= $\sqrt{(7)^{2} + (4)^{2} + ( - 5)^{2}} = \sqrt{49 + 16 + 25}$= √90 = 3√10m