Question
Find the vector equation of the plane determined by the points (1, 0,−1), (0, 1, 1) and (−1, 1, 0). Also find the point of intersection of the line
Answer :
Word Count : 256
To find the vector equation of the plane determined by the points $A(1, 0, -1)$, $B(0, 1, 1)$, and $C(-1, 1, 0)$, we first determine two direction vectors lying on the plane. Let $$ \vec{AB} = \vec{B} - \vec{A} = (0-1, 1-0, 1-(-1)) = (-1, 1, 2) $$ $$ \vec{AC} = \vec{C} - \vec{A} = (-1-1, 1-0, 0-(-1)) = (-2, 1, 1) $$ The ______ _____ ___ __________ ______ _______ ________ __________ ________ ______ ________ _____.
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To find the vector equation of the plane determined by the points $A(1, 0, -1)$, $B(0, 1, 1)$, and $C(-1, 1, 0)$, we first determine two direction vectors lying on the plane. Let $$ \vec{AB} = \vec{B} - \vec{A} = (0-1, 1-0, 1-(-1)) = (-1, 1, 2) $$ $$ \vec{AC} = \vec{C} - \vec{A} = (-1-1, 1-0, 0-(-1)) = (-2, 1, 1) $$ The ______ _____ ___ __________ ______ _______ ________ __________ ________ ______ ________ _____.
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Related Questions
a) Check whether the matrices
a) Consider the following system of equations:
a) For the vector space
a) Let
Let
Which of the following statements are true and which are false? Justify your answer with a short proof or a counterexample.
i) The Row Reduced Echelon form of any invertible square matrix is the identity matrix
dim(W1) dim(v)/2,dim(W2)
dim(v) /2 ,the W1 ∩ W2
{0}.
iii) If
b) Let
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