Find two vectors ₁ and ₂ whose sum is (-3, -2), where №₁ is parallel to (5,-5) while 72 is perpendicular to (5, -5). V1 = V₂ = and
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- Find the dot product of the pair of vectors (-2, 5) and (4, 1).Let a, b, and x denote vectors in R,,. (a) Simplify 3a + (5b -2a) + 2(b - a). (b) If 5x - a = 2(a + 2x),solve for x in terms of a.Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector product of the vectors (1,3, -5) and (-3,1,4).
- Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors {(1,-2,2),(0,5,5), (2,0,8)}? Either write the linear combination or explain why you can’t.Find the vector in the same direction as <1, 1, 0> whose component in the direction of <2, 0, -4> is unity.Find a general set of solution vectors x₂ = - 5x2 X₂ = x₁ + 3x₂
- Determine the area of the parallelogram determined by the vectors ⟨5, 3 ⟩ and ⟨−8, −1 ⟩. Determine the area of the parallelogram determined by the vectors ⟨−5, 8, 9 ⟩ and ⟨6, 2, 9 ⟩.a = (4, 3), b = (4, -3), c = (-3, 4) and d = (-3, -4) Which of the following pairs of vectors is perpendicular?Q3/ Let å = (2,1, -4) and b = (3,-2,5) be two vectors. Find a vector that perpendicular to both å and b.