The unit vector perpendicular to both vectors \hat{i} + ...

CBSE Class 12 Math 2024 All Sets Solved Paper

Question : 15 of 20

Marks: +1, -0

The unit vector perpendicular to both vectors

{i}↖{∧} + {k}↖{∧}

and

{i}↖{∧} - {k}↖{∧}

Solution:

Formula to be used:

{n}↖{→} = {a}↖{→} × {b}↖{→}

and

{n}↖{∧} = \;{{n}↖{→}}/{ | {n}↖{→} | }

where it is the unit vector perpendicular to both vectors

{a}↖{→}

and

{b}↖{→}

{n}↖{→} = ({i}↖{∧} + {k}↖{∧}) × ({i}↖{∧} - {k}↖{∧}) = {|\table {i}↖{∧} , {j}↖{∧}, {k}↖{∧};1,0,1;1,0,-1 |} = -{j}↖{∧} (-1 -1) = 2 {j}↖{∧}

{n}↖{∧} = \;{2 {j}↖{∧}}/{√ {2^2}} = {j}↖{∧}

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