If the vector Kâ- +Lây+ M â, shows the maximum increase rate and direction of the scalar V at point P(8 ,7, 14) at which V= 16,6xy+17,9 xyz, find K =?. Yanıt:
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A: a) The given vectors are, Analyze the following figure representing the given vector.
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- For the vectors A=2i + 3j, B= 3j- 5k and C= -4i + k. Find: A) V= A-B+C B) V C) vGiven two vector A = -5.00i –- 9.00j + 4.00k and B = -4.00i + 6.00j – 2.00k what is the vector product A × B.Vector A = 3 i + 3.8 j. Vector B = 5.1 i - 7.5 j. The dot product of the two is C = A ∙ B (i.e. A dot B). The value of C is:
- Given M = 6 î + 5 j – 6 k and N = 3 î - 3 j - 3 k, calculate the vector product M x N. j +Two vectors have the following magnitude, A = 8.9 m and B = 7 m. Their vector product is: A⨯B = -1.8 m i + 13.8 m k. What is the angle (in degrees) between the vectors A and B?Problem 2: Given vectors: A = 3 i+j- k, B = - i+ 2j+ 5 k, C = 2 j - 3 k. Find: 1. C. (A + B) 2. Cx (A - B)
- Two vectors have the following magnitude, A = 8.7 m and B = 10.6 m. Their vector product is: A:B = -2.7 m i+ 8.6 m k. What is the angle (in degrees) between the vectors A and B? Hint: Use |A:B| = AB sin(0) Note: Bold face letters represents a vector.Given the pair of vectors, A = (9.00î − 5.00ĵ ) and B =(−3.00î + 9.00ĵ ),use the definition of a scalar product to determine the following. (a) the scalar product (b) the angle between the vectors (Enter an answer between 0 and 180 degrees.) ° (c) the angle ? between the vector A and the +x axis (Enter an answer between 0 and 180 degrees.) ° (d) the angle ? between the vector B and the +y axis (Enter an answer between 0 and 180 degrees.) °Use the definition of scalar product, a = ab cos 0, and the fact that a . the two vectors given by a = 3.01 +3.0 + 3.0k and b Number i Units = axbx + ab + a₂b₂ to calculate the angle between 4.0î + 9.0ĵ + 7.0k. =
- The Scalar Product The vectors A andB are given by A = 31 + 1j and B = -1î + 1j. (a) Determine the scalar product A - B. SOLUTION Conceptualize There is no physical system to imagine here. Rather, it is purely a mathematical exercise involving two (vectors Categorize Because we have a definition for the scalar product, we categorize this example as a substitution vy problem. Substitute the specific vector expressions for A and B: A-B = (31 + 1j) - (-1î + 1j) = [3i - (-1)i - [31 - 15 - 13 - (-1) + [1j - 15] The same result is obtained when we use the equation A -B = AB, + A8, + A,B, directly, where A, = 3, A, = 1, B, = -1 and 8, = 1. (b) Find the angle e between A and B. SOLUTION Evaluate the magnitudes of A and B using the Pythagorean theorem: A = VA,? + A, = B = V82 + B 2 = Use the equation A - B = AB cos(e) and the result from part (a) to find the angle (in degrees). cos(e) = AB EXERCISE As a particle moves from the origin to (7i + 5j) m, it is acted upon by a force given by (7î +…Let the x-, y-, and z-axes be identified as axes 1, 2, and 3, respectively. Find the angle between A and axis 2 if A=0.17, Ay = 2.76, and A₂ = 2.98. [Hint: Write the unit vector in the direction of axis 2 and use A. B = A₂ B₂ + A, B, + A₂B₂ = AB cos 1 Φ Record your numerical answer below, assuming three significant figures. A(6%) Problem 5: Consider the following vectors: A = 4.6i + 1.4j+ 3.4k В = -6. 5i + 7.1j + 10.2k 25% Part (a) What is the x-component of the vector V = 3(A × 2B)? Vx= sin() cos() tan() 7 8 9 НOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 cosh() tanh() cotanh() + END Degrees Radians Vd BACKSPACE DEL CLEAR Feedback Submit Hint I I give up! Hints: 2 for a 0% deduction. Hints remaining: 0 Feedback: 3% deduction per feedback. -This is a cross-product, so the answer will be a vector. In this part, we just want the x-component of the vector. Keep in mind that scalars like "2" and "3" distribute 3.