solve Graded Homework 1- This homework covers Sections 12.3 ndash 12.5 and is du

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Graded Homework 1- This homework covers Sections 12.3 ndash 12.5 and is due at the end of class Tuesday January 21st. Each question is 5 points each. Find both two-dimensional vectors which have length root 10 and are perpendicular to . Let and be vectors. Show that Where does the line through (1,0,1) and (4,-2,2) intersect the plane x + y + z = 8? Graded Homework 2- This homework covers Section 13.4 and is due at the end of class Monday January 27th. The value of each question is listed by the question.

Explanation / Answer

1) suppose vector be xi + yj

then x^2 + y^2 = 10

& x + 3y = 0

=> y = 1, -1 & x = -3,3 hence vectors are (-3i + j) & (3i - j)

2) |a x b| = |a||b| sina

and , -1<= sina <= 1

hence |a x b| <= |a||b|

3) line through (1,0,1) & (4,-2,2) be like

i + k + t(3i -2j + k)

hence parametric form will be

x = 1 + 3t

y = -2t

z = 1 + t

it passes through plane => 1 + 3t -2t + 1+ t = 8

hence t = 3

therefore x = 4, y = -6, z = 4

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