CBSE Class 12 Maths 2010 Solved Paper

Question : 5 of 29

Marks: +1, -0

Write a vector of magnitude 15 units in the direction of vector

i↖{\^}-2j↖{\^}+2k↖{\^}

Solution:

Unit vector along the direction of vector

a↖{→}

a↖{→}

a↖{→}/{|a↖{→}|}

Let

a↖{→}

i↖{\^}-2j↖{\^}+2k↖{\^}

|a↖{→}|

√{(1)^2+(-2)^2+(2)^2}

= ± 3
i.e.

a↖{\^}

1/3 (i↖{\^}-2j↖{\^}+2k↖{\^})

So, the vector whose magnitude is 15 and has direction along the vector

i↖{\^}-2j↖{\^}+2k↖{\^}

is given by,
15 ×

(1/3)(i↖{\^}-2j↖{\^}+2k↖{\^})

= 5

(i↖{\^}-2j↖{\^}+2k↖{\^})

(5i↖{\^}-10j↖{\^}+10k↖{\^})

So the required vector is

(5i↖{\^}-10j↖{\^}+10k↖{\^})

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