Unit vector \overrightarrow{PQ}, where coordinates of P and ...

CBSE Class 12 Math 2023 All Sets Solved Paper

Question : 4 of 20

Marks: +1, -0

Unit vector

{PQ}↖{→},

where coordinates of P and Q respectively are (2, 1, -1) and (4, 4, -7), is

Solution:

{P Q}↖{→}={O Q}↖{→}-{O P}↖{→}

=(4 {𝑖}↖{∧}+4 {𝑗}↖{∧}-7 {k}↖{∧})-(2 {𝑖}↖{∧}+{𝑗}↖{∧}-{k}↖{∧})

=2 {𝑖}↖{∧}+3 {𝑗}↖{∧}-6 {k}↖{∧}

| {P Q}↖{→} | =√{2^{2}+3^{2}+(-6)^{2}}=7

Unit vector along

{PQ}↖{→}

{a}↖{∧}=\;{{PQ}↖{→}}/{ | {PQ}↖{→} | }

=\;{2 {i}↖{∧}}/{7}+\;{3 {j}↖{∧}}/{7}-\;{6 {k}↖{∧}}/{7}

Go to Question:

Prev Question

Next Question