Question 3 Determine for what values of the parameter a ? the following planes i

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Question 3

Determine for what values of the parameter a ? the following planes in R^3R 3 are perpendicular

eq1: ax - 20y + 10z = -1

ew2: ax + ay + 10z = -15.

?x?20y+10z=?1, ?x+?y+10z=?15. Write your answer in the form { a,b} or { a}{a} ?x?20y+10z=?1, ?x+?y+10z=?15. Write your answer in the form { a,b} or { a}{a} ?x?20y+10z=?1, ?x+?y+10z=?15. Write your answer in the form { a,b} or { a}{a} ?x?20y+10z=?1, ?x+?y+10z=?15. Write your answer in the form { a,b} or { a}{a} ?x?20y+10z=?1, ?x+?y+10z=?15. Write your answer in the form { a,b} or { a}{a}

Explanation / Answer

for plane 1, normal vector n1= <a, -20,10>

for plane 2, n2= <a,a,10>

for the planes to be perpendicular, n1.n2=0

=> <a, -20,10> . <a,a,10> =0

=> a^2 -20a +100=0

=> (a-10)^2 =0

=> a=10

{a,a} = {10,10}

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