CBSE Class 12 Math 2012 Solved Paper - Question 11 | ExamSiri

CBSE Class 12 Math 2012 Solved Paper

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Question : 11 of 29

Marks: +1, -0

If

a↖{→},b↖{→},c↖{→}

are three vectors such that

|a↖{→}|

= 5 ,

|b↖{→}|

= 12 and

|c↖{→}|

= 13 and

a↖{→}+b↖{→}+c↖{→}

= 0. Find the value of

a↖{→}.b↖{→}

+

b↖{→}.c↖{→}

+

c↖{→}.a↖{→}

Solution:

Considering dot product on both sides,

(a↖{→}+b↖{→}+c↖{→})

.

(a↖{→}+b↖{→}+c↖{→})

= 0 . 0
⇒

|a↖{→}|^2+|b↖{→}|^2+|c↖{→}|^2

+ 2

(a↖{→}.b↖{→}

+

b↖{→}.c↖{→}

+

c↖{→}.a↖{→})

= 0
⇒

5^2+12^2+13^2

+ 2

(a↖{→}.b↖{→}

+

b↖{→}.c↖{→}

+

c↖{→}.a↖{→})

= 0 = 0
⇒ 2

(a↖{→}.b↖{→}

+

b↖{→}.c↖{→}

+

c↖{→}.a↖{→})

= - 388
⇒

(a↖{→}.b↖{→}

+

b↖{→}.c↖{→}

+

c↖{→}.a↖{→})

= -

{338}/2

= - 169

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