Scalar Vector |a|.|b|=0? Help please!

Question

(i) The two vectors a = (4, p, q) and b = (q, -5, p) are perpendicular.
Write an equation that includes both p and q .

(ii) The modulus | a | is sqrt61 . Write, and simplify, another equation that includes both p and q , and use it to obtain the length of vector b .

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Answer 1 · 2018-02-25T19:16:58

Kindly refer to the Explanation.

Part (i) :

#veca=(4,p,q) bot vecb=(q,-5,p) rArr veca*vecb=0#.

#:. 4(q)+p(-5)+q(p)=0#.

#:. 4q-5p+pq=0...(1)#, is the desired eqn. in #p and q#.

Part (ii) :

Given that, #|veca|=sqrt61#, we have,

#sqrt(4^2+p^2+q^2)=sqrt61, or, #

#sqrt(16+p^2+q^2)=sqrt61#.

#rArr 16+p^2+q^2=61, or, #

# p^2+q^2=45............(2)#.

Finally, to obtain the length #|vecb|" of "vecb=(q,-5,p)#, we have,

#|vecb|=sqrt{q^2+(-5)^2+p^2}#,

#=sqrt(p^2+q^2+25)#,

#=sqrt(45+25)............[because, (2)]#,

#rArr |vecb|=sqrt70#.