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the vector P=ai+aj+3k and Q=ai-2j-k are perpendicular to each other. the positive value of a is :
* As P and Q are perpendicular to each other their DOT PRODUCT or SCALAR PRODUCT will be o.*
(P).(Q)=(ai+aj+3k).(ai-2j-k) [I hope you know what is dot product and how to solve it]
=>a2_2a-3
=a(a-3)+1(a-3)
=(a+1)(a-3)
=> a=-1 or 3
POSITIVE VALUE=3
a=-1 or a=3
by using MOD( Pvector +Q vector ) = √(P2 +Q2)
Since both the vectors are perpendicular to each other therefore there dot product will be zero. because cos90=0
now p.q=0
(ai+aj+3k).(ai-2j-k)=0
a2 - 2a - 3 =0
a2 -3a + a -3=0
a(a-3)+1(a-3)=0
(a+1)(a-3)=0
therefore .. a=-1 or a=3
since the vectors are perpendicualr their scalar product is zero.
this gives the quadratic equation a2 - 2a - 3 = 0
so the positive value of a is 3.
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