1. Let a= (<5,3>) and b= (<1,-1>). Show that there are scalars s and t so that sa + sb=(<-3,-5>) 2. A child walks due east on the deck of a ship at 3 miles per hour. The ship is moving north at a speed of 1 miles per hour. Find the speed and direction of the child relative to the surface of the water. 3. A horizontal clothesline is tied between 2 poles, 10 meters apart. When a mass of 2 kkilo grams is tied to the middle of the clothesline, it sags a distance of 4 meters. What is the magnitude of the tension on the ends of the clothsline?

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) +…

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Q: Hiwil show that_Viz 3i+6j_and_V=-i-zj have offosite direction.

A: We have to prove that vectors have opposite direction.

Q: Find a scalar equation of the plane containing the line and the point (-5, -1,5). x = 6 +8t, y=-1-3t…

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Q: Given a point M = (5,–3,–2) on a line in space and a parallel vector to the line defined as vector d…

A: Parametric equations of a line  in 3-D space are given byx = x0 + t a , y = y0 + t b , z = z0 + t c…

Q: Let L be the line with parametric equations x-2-2t y-10-2t 2-8-21 Find the vector equation for a…

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Q: Explain the term scalar.

A: Explanation: Given that, term scalar.

Q: A bee starts at the point (5, 7, -3) (with units in meters) and travels at a constant speed of 9 m/s…

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Q: 4

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Q: Find the scalars if they are linearly dependent.

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Q: Let u= (2,-3, 2, 5) and v a- i b- = (1, 2, 0, -4). Find scalars a and b so that au + bv = (0, -7,2,…

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Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

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Q: Write the parametric equations of the line through the point (1,2,3) parallel to the vector a =.…

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Q: Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes…

A: Given: Line A passes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A. Line…