Question Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as – 2i + 9j. u = (b) Oppositely directed to 12i – 8j + 8k. V (c) Same direction as the vector from the point A(-1,0,2) to the point B(3,1,1). W =

PDND5J The Asker · Calculus

Transcribed Image Text: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as – 2i + 9j. u = (b) Oppositely directed to 12i – 8j + 8k. V (c) Same direction as the vector from the point A(-1,0,2) to the point B(3,1,1). W =
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Transcribed Image Text: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as – 2i + 9j. u = (b) Oppositely directed to 12i – 8j + 8k. V (c) Same direction as the vector from the point A(-1,0,2) to the point B(3,1,1). W =
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HBCLOU

Solution: (a) Given that the vector -2 hat(i)+9 hat(j)" Now "{:[|-2 hat(i)+9 hat(j)|=sqrt((-2)^(2)+(9)^(2))],[=sqrt(4+81)=sqrt85.]:}since vec(a)=x_(i)+y hat(j) then | vec(a)|=sqrt(x^(2)+y^(2)).:. The unit vectors in the same livection of -2 hat(i)+9 hat(j) is quad(-2( hat(i))+9( hat(j)))/(1-2( hat(i))+9( hat(j)))=(-2( hat(i))+9( hat(j)))/(sqrt85)Hence vec(u)=(-2( hat(i))+9( hat(j)))/(sqrt85)(b) Given that the vector 12 hat(i)-8 hat(j)+8 hat(k).{:[:.|12 hat(i)-8 hat(j)+8 hat(k)|=sqrt((12)^(2)+(-8)^(2)+8^(2))],[=sqrt(144+64+64)=sqrt272=4sqrt17.]:}Hence the required unit vector oppositely directed to 12 hat(i)-8 hat(j)+8 hat(k) is-(12( hat(i) ... See the full answer