Question
Find a unit vector in the direction of $\overrightarrow {P{\rm{Q}}}$, where $P$ and $Q$ have coordinates (5,0,8) and $(3,3,2)$, respectively.
Since, the coordinates of $P$ and $Q$ are (5,0,8) and (3,3,2) , respectively.
Vector Algebra — Class 12 Maths Solution
Step-by-step Solution
$\therefore$ $\overrightarrow {PQ} = \overrightarrow {OQ} - \overrightarrow {OP}$
$= (3\widehat {\rm{i}} + 3\widehat {\rm{j}} + 2\widehat {\rm{k}}) - (\widehat {\rm{i}} + 0\widehat {\rm{j}} + 8\widehat {\rm{k}})$
$= - 2\widehat {\rm{i}} + 3\widehat {\rm{j}} - 6\widehat {\rm{k}}$
$\therefore$
Unit vector in the direction of $\overrightarrow {{\rm{PQ}}} = \frac{{\overrightarrow {{\rm{PQ}}} }}{{|\overrightarrow {{\rm{PQ}}} |}} = \frac{{ - 2\widehat {\rm{i}} + 3\widehat {\rm{j}} - 6\widehat {\rm{k}}}}{{\sqrt {{2^2} + {3^2} + {6^2}} }}$
$= \frac{{ - 2\widehat {\rm{i}} + 3\widehat {\rm{j}} - 6\widehat {\rm{k}}}}{{\sqrt {49} }}$
$= \frac{{ - 2\widehat {\rm{i}} + 3\widehat {\rm{j}} - 6\widehat {\rm{k}}}}{7}$
NCERT & Exemplar solution for CBSE Class 12 Mathematics, Vector Algebra. Curated by Sachin Sharma. Free for all students.