Find a unit vector in the direction of a^{\to} = 3i^{\^} -2j^{\^} + 6k^{\^}

CBSE Class 12 Math 2008 Solved Paper - Question 8

Question : 8 of 29

Marks: +1, -0

Find a unit vector in the direction of

a↖{→}

3i↖{\^} -2j↖{\^} + 6k↖{\^}

Solution:

The unit vector

(a↖{\^})

in the direction of

a↖{→}

is given by

a↖{→}{|a↖{→}|}

a↖{\^}

{3i↖{\^}-2j↖{\^}+6k↖{\^}}/√{3^2+(-2)^2+6^2}

{3i↖{\^}-2j↖{\^}+6k↖{\^}}/√{9+4+36}

{3i↖{\^}-2j↖{\^}+6k↖{\^}}/√{49}

1/7

[

3i↖{\^} -2j↖{\^} + 6k↖{\^}

]
=

3/7i↖{\^}-2/7j↖{\^}+6/7k↖{\^}

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