Homework answers / question archive / Given the figure below, find the component form of the vector ? + w if ? and ? are unit vectors: Y 135° ? 30° T Find a unit vector oppositely oriented to the vector ?= (6, -4,2)

Given the figure below, find the component form of the vector ? + w if ? and ? are unit vectors: Y 135° ? 30° T Find a unit vector oppositely oriented to the vector ?= (6, -4,2)

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Given the figure below, find the component form of the vector ? + w if ? and ? are unit vectors: Y 135° ? 30° T Find a unit vector oppositely oriented to the vector ?= (6, -4,2). 8 Find a vector ? with magnitude 6 in the direction of the vector that has initial point A(-1,0, 2) and terminal point B(3, 1, 1). 9 Determine whether the following vectors are coplanar: ?= 3î + î+2î, = (4,5,1), and ? = î+2?+4î. 10 Let ? = (2,-1, 3) and W = (2,0, -1). (a) Find the vector component of ? along the vector W. (b) Find the vector component of ? along the vector ? + 2?. (c) Find projw? and proj7c. 1 Let ?= 3î + 2? +, = î + û + 2k, and = î +3î + 3Â be adjacent edges of a parallelepiped. (a) Find the volume of the parallelepiped. (b) Find the area of the face determined by ? and w. (c) Find the angle between ? and the plane containing the face determined by ? and w. 2 Let O be the angle between vectors ?= 2î + 3? + 6î and ?= 3î + 29 – ?. (a) Use dot product to find cos 0. (b) Use the cross product to find sin 0. (c) Confirm the identity sin? 0 + cos² 0 = 1. 3 Find two unit vectors that are orthogonal to the plane determined by the points A(0, –2, 1), B(1,-1, -2), and C(-1,1,0). 4 Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector ? = (3, -1,3). 5 Given the figure below, find the magnitude of the resultant force and the angle that it makes with the positive x-axis: Y 100N 60° 120N