Do not solve just prove using grade 12 knowloge No matrix  3. Show that the planes below form a triangular prism. Determine a direction vector with integer components for the line of intersection for each pair o f planes : x + y – z + 2 = 0 2 x + 2 y – z – 6 = 0 4 x + 4 y – z + 5 = 0

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Given two non-zero vectors a and b such that abs(a+b)=abs(a-b), find the value of a*b (dot product…

A: Given Two non-zero vectors a and b such that  a+b=a-b            ...........1 The dot product of and…

Q: linear Consider the following vectors in R³: V= (-1,7,2), u₁₁ = (1,3,5) U1₂ = (2₁-1₁3), (13=…

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Q: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q5) the value of the constant a for which the line x=2+t,y=2+3t,z=3+t and the plane ax+y-2z-7=0 are…

A: We will use definition.

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A: Let  be vectors.(A) To find the scalar projection of .(B) To decompose the vector  into a component…

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Q: what is the graph of vector B = C - A??

A: First we mark A and C vectors then we find -C vector  The resultant of A and -C will be B as B = A -…

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Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

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Q: Find the B-coordinate vector for p(t) = -6+10t-7t² B={1-2t+t², 4-7t +5t², 5-8t+8t²} Enter your…

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Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: If V1 = [1 4 0] and V2 = [ -2 0 8], then determine all possible 1x3 row vectors V3 such that the set…

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Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Can it be fit diagonally ?

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