If \stackrel{\^}{i}, \stackrel{\^}{j}, \stackrel{\^}{k} are unit vectors along three mutually perpendicular directions, then

\stackrel{\^}{i} \cdot \stackrel{\^}{j}=1

\stackrel{\^}{i} \times \stackrel{\^}{j}=1

\stackrel{\^}{ {\i}} \cdot \stackrel{\^}{ {\k}}=0

\stackrel{\^}{ {\i}} \times \stackrel{\^}{ {\k}}=0

CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper - Question 5

Question : 5 of 36

Marks: +1, -0

{i}↖{\^}, {j}↖{\^}, {k}↖{\^}

are unit vectors along three mutually perpendicular directions, then

Solution:

Given,

{𝑖}↖{\^}, {𝑗}↖{\^}, { {\K}↖{\^}}

are vectors and mutually perpendicular to each other
Here

{𝑖}↖{\^} {i}↖{\^} {𝑗}↖{\^}={𝑗}↖{\^} . {k}↖{\^}={k}↖{\^} ⋅ {𝑖}↖{\^}=0

and

{i}↖{\^} × {j}↖{\^}={k}↖{\^}

{j}↖{\^} × {k}↖{\^}={i}↖{\^}

{k}↖{\^} × {i}↖{\^}={j}↖{\^}

∴

Only option

[ {\C}]

î.

{ {\K}↖{\^}}=0

is the correct answer

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