Concept explainers
Compute the dot product A - B for each of the following cases. Identify the units of each product.
(a)
The dot product
Answer to Problem 1.57P
The dot product
Explanation of Solution
Given that:
Concept: - We know that the dot product
Calculation: -
The dot product
(b)
The dot product
Answer to Problem 1.57P
The dot product
Explanation of Solution
Given that:
Concept: - We know that the dot product
Calculation: -
The dot product
(c)
The dot product
Answer to Problem 1.57P
The dot product
Explanation of Solution
Given that: -
Concept: - We know that the dot product
Calculation: -
The dot product
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Chapter 1 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- For the section to the right, find the neutral axis due to the applied moment. (a) First work the problem in x'- y coordinate system. (b) Then work the problem in x-y coordinate system and show the final location of the neutral axis is the same. 5 mm M = 400 N·m 18.57 mm 30° 5 mm 50 mm 5 mm 50 mm Oarrow_forwardThe displacement vectors A and B shown in the figure below both have magnitudes of 3.10 m. The direction of vector A is 0 = 23.0°. (a) Find A + B graphically. magnitude m direction o counterclockwise from the +x axis (b) Find A – B graphically. magnitude direction o counterclockwise from the +x axis (c) Find B - A graphically. magnitude direction o counterclockwise from the +x axisarrow_forwardIf A = 2i + 4 j - 5 k, the the direction of cosines of the vector A are * 0.298, 0.596, -0.745 0.149, 0.298, 0.447 0.149, 0, 0.596 O 0.447, 0.298, 0.745arrow_forward
- 4.2:As shown in the figure at a point A, since the unit extensions in three directions with 120◦ between them are Ꜫa = 430.10-6 Ꜫb= 260.10-6 Ꜫc= 590.10-6 , find the largest and smallest angle changes with their directions. Answer:ψ1=-0.5◦ ,ꝩmax= 381.10-6,ψ2=89.5◦ ,ꝩmin= -381.10-6arrow_forwarda = 1.2 m b = 1.8 m C= 4 m Force AB = 500 Newtons FAB A Find the z-component of unit vector AB. (Hint: the value should be less than 1). If the calculated answer is not whole number, express it in 4 significant figures. If the value is negative, include a negative sign. Find the Length of AC in m. Find the x-component of unit vector AC. (Hint: the value should be less than 1).arrow_forwardFind unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i, j and k. (a) Same direction as - 2i + 5j. u = (b) Oppositely directed to 9i – 6j + 6k. (c) Same direction as the vector from the point A(-2,0, 4) to the point В(3, 3, 3). w =arrow_forward
- V4 + x lim 2 |arrow_forwardsec. 4-2 Position and Displacement •1 The position vector for an electron is 7 (5.0 m)i – (3.0 m)j + (2.0 m)k. (a) Find the magnitude of r. (b) Sketch the vector on a right-handed coordinate system.arrow_forwardA force couple acting on the rod. Find: The couple moment acting on the rod in Cartesian vector notation. F= (-14i + 8j + 6k)N 0.5 m 0.8 m 1.5 m 0.5 m F = (14i - 8j - 6k )Narrow_forward
- The magnitude of two vectors A and B shown in the figure below are respectively A = 3m and B 1.5 m. The magnitude(R) and the direction (6) of their resultant R = A+ B are equal to: R= 1.239 m e = 43.29 degree R = 1.859 m ; 0 23.79 degree R = 1.239 m; 6e 23.79 degree R = 1.859 m;e = 43.29 degree R = 0.620 m;e = 23.79 degreearrow_forwardA point is located in a polar co-ordinate system by the co-ordinates r = 2.5 m and 0= 35°. Find the x- and y co-ordinates of this point, assuming that the two co-ordinate systems have the same origin.arrow_forwardASAParrow_forward
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