1 1. Let Ẩ = (1, -2, 4) and B be a nonzero vector parallel to 0, 3 2' 2 a. Find the vector projection of Bonto A without finding the components of B. b. Find the components of B. Hint: Note that two nonzero vectors are parallel when one of them is a scalar multiple of the other. Also, use a property of the dot product. such that AB = 14. c. Using A and the result of item 1(b), find a set of parametric equations for the line with direction vector A+ 4B that passes through the point (4,3,5).

Q: Compute the following cross product. Then make a sketch showing the two vectors and their cross…

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Q: Find the dot product of vectors and .

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Q: Calculate the cosine of the angle which the vector 2i+2j-k makes with the positive x-axis

A: Given: find the cosine of the angle which the vector 2i+2j-k makes with positive x axis

Q: Express the vector as a product of its length and direction. 21+4j+4k O A. 6 OB. 6 18 + gi+? OC.…

A: The given vector is  2i + 4j + 4k we have to express vector as a product of its length and…

Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: Q2. What will be the effect of multiplying the vector by a positive and a negative scalar. Explain…

A: To find: The effect of multiplying a vector by a positive and a negative scalar.  Explanation: When…

Q: Determine the vector 2a – b if a = -4i + 5j and b = 7i + 2j. %3D

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 3v - 4w.

A: Given  u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. We need to find the specified vector or scalar…

Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar l-l-2ul.

A: Here given as u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Thus -2u=-2·2i+2·5j=-4i+10j