Consider the points A(1,−3,4), B(2,5,4) and C(1,1,6). Then the cross product AB × AC is the vector:   Hence the equation of the plane passing through the points A(1,−3,4), B(2,5,4) and C(1,1,6) is given by:

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A: Sol

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A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

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Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

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A: For orthogonal,dot product of vectors is equal to zero.

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A: To find the vector in component form that is perpendicular to the given line.

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A: Solution is here

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A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

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A: Given point A and B. Find vector AB.

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A: Explanation of the answer is as follows

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A: Hi there, At a time we can answer only one question. So, I have answered first one (#6).

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Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

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A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

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A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

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A: find the explanation below

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector