MATH 153E
QUIZ 10
math线上代考 Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, -1), B(3, -2, 0), C(1, 3, 3).
Take-Home Quiz 15 (Total 15p.) Show your work! math线上代考
- (2p.) Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, -1), B(3, -2, 0), C(1, 3, 3).
- (1p.) Determine whether the given vectors are orthogonal, parallel, or neither. a = 3i – j + 3k, b =5i + 9j – 2k
- (2p.) Find two unit vectors orthogonal to both <3,2,1> and <-1,1,0>.
- (2p.) Find the acute angles between the curves at their points of intersection. (The angle between two curves is the angle between their tangent lines at the point of intersection.) y = sin x, y = cos x, 0 ≤ x ≤ ?/2.
- (1p.) Find the vector, not with determinants, but by using properties of cross products. ( j – k) × (k – i).
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(2p.) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR: P(0, -2, 0), Q(4, 1, -2), R(5, 3, 1). math线上代考
- (2p.) Use the scalar triple product to verify that the vectors u = i + 5 j – 2 k, v = 3i – j, and w = 5i + 9 j – 4 k are coplanar.
- (1p.) A wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction <0, 3, -4 > at the end of the wrench. Find the magnitude of the force needed to supply 100 N∙m of torque to the bolt.
- (2p.) If a∙b = √3 and a × b = <1, 2, 2 >, find the angle between a and b.
