2- if Å = 3i – j – 4k, B = –2i + 4j – 3k, Č = i + 2j – k, D = ai – 3j – 3k find : (d) B · Č (e) à · B × ċ (), А x (В x C) (в) (А х В) х С (h) angle between à · Č (i) value of 2 that makes the vectors D· C orthogonal. (j) The area of a parallelogram that B· C are Two adjacent sides on it. (k) value of 2 that makes the vectors D· Á orthogonal. (h) the component of Ả in direction of B.
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- Question 30 In a "left handed" plane polar coordinate system, the position P(r,0) is defined in terms of r and 0 where r is the magnitude of the position vector i and 0 is the angle between i and y- axis measured from'y-axis as seen in the figure. (a) Express the positon vector i in this "left handed" plane polar coordinates (LHPPC). (b) Show the f and ô unit vectors of this LHPPC. Show them in a graph such as the one given on the left. Also express them in terms of the unit vectors of Cartesian coordinates. dr (c) Calculate an expression velocity v = as a function dt of r and 0 in LHPPC. (d) Calculate the expression for acceleration a(r,0) in LHPPC.In the cross (or vector) product F= qu x B we know that q=1 F = -301 +9.07+-21k U= -3.07+4.00 +6.0 B=B₁1+B) + BA What then is B in unit-vector notation if B,-8,7 B ÂUse the definition of scalar product, a · b = ab cos 0, and the fact that a = axbx + ayby + ażbz to calculate the angle between the two vectors given by á 8.0î + 8.0 + 8.0k and b = 7.0î + 8.0j + 6.0k. Number 168 Units ° (degrees)
- = 2. At any point of the curve x 3 cos t, y = 3 sin t, z = 4 t, find (i) Tangent vector (ii) Unit tangent vectorIf v=a Subscript 1i+b Subscript 1j and w=a Subscript 2i+b Subscript 2j are vectors, the product v•w, called the _______, is defined as v•w=_______.If vector Á has components Ax = -3.0 lb and Ay = -4.0 lb, and vector has components Bx = 3.0 Ib and By = -8.0 lb, what is the %3D magnitude of vector ć = Á 140 Ib - в ? 7.2 lb О 13 1b 16 Ib
- Suppose U and V are unit vectors in R" and ||U – aW|| = 6 and angle between U&W is 90°, then the value of a is2)Given the vectors A =3 î +2 ĵ and B = î -3ĵ a-Calculate the vector sum M=A+B and the vector difference N= A-B in terms of unit vectors. b- Find the direction and magnitude of the vectors M and N. 3)The polar coordinate of (r, θ ) of a Cartesian coordinate (-3.5,-2.5) is: a) (4.3, 216o ) b) (10, 100o ) c) (120, 17o ) 4)Two vectors are given as a= i +2j+2k and b=2i+4j+2k . Vector c which satisfies the relation a-b+c=3i is: a) i+3j b) –i +j c) -i+5j d) 4i+2j5. Let A = (2 m) + (6 m)-(3 m)k and B = (4 m) + (2 my +(1 m). The vector difference D = A -B A) (6 m) + (8 my - (2 myk B) (-2 m + (4 my - (4 my -(4 m) (2 m) - (4 m) + (4 m)* D) (8 m) + (12 m -(3 m) E) none of these
- 5. If A = 3å + 2ŷ + 22 and B = 20 + 3ŷ - 2, find (a) Ã× B (b) The unit vector pointing in the direction of Ä× B IfGiven vector A = <2, -5, -24> and vector B = <6, 15, 20> , what is the magnitude of A x B?What is the sum of the following four vectors in (a) unit-vector notation, and as (b) a magnitude and (c) an angle? Positive angles are counterclockwise from the positive direction of the x axis; negative angles are clockwise. À = (2.00 m )i + (3.00 m )} B = 4.00 m, at 65.0⁰ 7 = ( - 4.00 m D = 5.00 m, at -235⁰ ¹)ì – (6.00 m )Ĵ