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- Q3/ Let å = (2,1, -4) and b = (3,-2,5) be two vectors. Find a vector that perpendicular to both å and b.Determine if the vectors < -2,-1,1>, <3,-4,-2> and <5,-10-8> are linearly independent.A rectangle is formed by the vectors (4,1) (1,3) and (3,3). Determine the area of the rectangle, explain briefly how you can determine it.
- Find the vector needed to translate from point (4,1) to point (8,3). Translate (-1,2) by the same vector.There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the vector (2,5,8) cannot be expressed in the form of a linear combination of these vectors, find it.Express the vector -9-7x- 15x² as a linear combination of p₁ = 2 + x +4x², p₂ = 1- x + 3x² and p3 3 + 2x + 5x²
- Write symmetric equations for the line that passes through the point (1,0,2) in the direction of the vector <2,-1,4>.Determine if vector (-5,11,-7) is in the span of the following set of vectors: {(1,-2,2),(0,5,5), (2,0,8)}. Show your work and explain what your work tells you for answering the question.
