1) Find a formula for the distance D between the point R(20.30) and the line ax
ID: 3210285 • Letter: 1
Question
1) Find a formula for the distance D between the point R(20.30) and the line ax + by + c = 0 2) Explain why each of the following expressions makes no sense 3) Show that A(2,-1,1), B(3, 2,-1), and C(7,0,-2) are vertices of a right triangle. At which vertex is the right angle? 4) Let i and u be nonzero vectors in R2 or R3, and let k = | and 1 = Ilvll. Show that the vector w = Iii + k bisects the angle between ti and it 5) Consider the set V = {xlx E R, x > 0), with operations rit z,-x1x2 and kr = rk with k E R . Show that V is a vector space. 6) Determine which of the following subsets are subspaces of PsCIR) a) All polynomials ao + aix + a2x2 + agE3 for which a,-0 b) All polynomials of the form a +a, where ao and ai are real numbers 7) Which of the following sets of vectors in R are linearly independent?Explanation / Answer
7Ans.
a) Let, a,b,c are some scalars.
a(2,-1,4)+b(3,6,2)+c(2,10,-4)=(0,0,0)
(2a,-a,4a)+(3b,6b,2b)+(2c,10c,-4c)=(0,0,0)
(2a+3b+2c,-a+6b+10c,4a+2b-4c)=(0,0,0)
By comparing, we get
2a+3b+2c=0
-a+6b+10c=0
4a+2b-4c=0
By solving above three equations we will get a=b=c=0.
Therefore (2,-1,4),(3,6,2),(2,10,-4) are linearly independent.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.