# the vector P=ai+aj+3k and Q=ai-2j-k are perpendicular to each other. the positive value of a is :

pranjal agarwal
10 Points
9 years ago

* 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

Bevkoof Singh
43 Points
9 years ago

a=-1 or a=3

by using    MOD( Pvector +Q vector ) = √(P2 +Q2)

Khushpreet Singh
33 Points
9 years ago

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

SOURAV MISHRA
37 Points
9 years ago

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.