The unit vector perpendicular to the vectors \hat{i}

CBSE Class 12 Math 2025 All Sets Solved Paper

Question : 2 of 20

Marks: +1, -0

The unit vector perpendicular to the vectors

{i}↖{∧} - {j}↖{∧}

and

{i}↖{∧} + {j}↖{∧}

Solution:

{a}↖{→}={i}↖{∧}-{j}↖{∧}

{b}↖{→}={i}↖{∧}+{j}↖{∧}

Let

{n}↖{∧}

be the unit vector perpendicular to both

{a}↖{→}

and

{b}↖{→}

{n}↖{∧}=\;{{a}↖{→} × {b}↖{→}}/{ | {a}↖{→} × {b}↖{→} | }

{{a}↖{→}} × {b}↖{→}=({i}↖{∧}- {j}↖{∧}) ×({i}↖{∧}+{j}↖{∧})

={|\table {i}↖{∧} , {j}↖{∧} , {k}↖{∧} ; 1 , -1 , 0 ; 1 , 1 , 0|}

{a}↖{→} × {b}↖{→}=2 {k}↖{∧}

| {a}↖{→} × {b}↖{→} | =2

{n}↖{∧}=\;{2 {k}↖{∧}}/{2}={k}↖{∧}

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