Question

the velocity of a particle is 3i+2j+3k.find the vector component of the velocity along the line i-j+k and its magnitude.

Answer 1

hope it will help u ...

Answer 2

Given:

Velocity = 3i+2j+3k

Line = i-j+k

Solution:

$Component\quad of\quad 3i+2j+3k\quad along\quad the\quad line\quad i-j+k\quad =\quad \frac { \left( 3i+2j+3k \right) \left( i-j+k \right) }{ \left| i-j+k \right|}$

$=\quad \frac { 3\quad -\quad 2\quad +\quad 3 }{ \sqrt { { 1 }^{ 2 }\quad +\quad { 1 }^{ 2 }\quad +\quad { 1 }^{ 2 } } }$

$=\quad \frac { 4 }{ \sqrt { 3 } }$

$\Rightarrow \quad Component\quad of\quad 3i+2j+3k\quad along\quad the\quad line\quad i-j+k\quad =\quad =\quad \frac { 4 }{ \sqrt { 3 } }$