Question

The length of the perpendicular from the origin to line is

• A. $2 \sqrt { 5 }$
• B. 2
• C. $5 \sqrt { 2 }$
• D. 6

Answer 1

Answer: (D)

6

Answer 2

$= 4 \mathrm { i } + 2 \mathrm { j } + 4 \mathrm { k } - \left( \frac { 12 + 8 - 20 } { 50 } \right) \cdot ( 3 \mathrm { i } + 4 \mathrm { j } - 5 \mathrm { k } )$

$\overrightarrow { \mathrm { PL } } = 4 \mathrm { i } + 2 \mathrm { j } + 4 \mathrm { k }$

The length of PL is magnitude of $\overrightarrow { P L }$ i.e.,

Length of perpendicular $= | \overrightarrow { P L } | = \sqrt { 16 + 4 + 16 } = 6$.