Question

Statics Note: Use g = 9.81 m/s when required. 3. Consider the vector A whose magnitude is 12 m. (a) Express A in terms of its Cartesian components. (4) (b) Hence calculate the angles that A makes with the pos- itiver and y axes. (2) 400

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Answer 1

Note : X axis is represented by vetor (i)

Y axis is represented by vector(j)

Z axis is represented by vector (k)

During Explanation , To represent Point A i have written : ( point A )

to represent Vector A i have written : ( A vector )

Solution :- how A vector in 3-1 can be represent Z Plu, y, z) N a a y X Figure - between rector P So here a Angle positive a-asis. ß is Angle between , vector P and tve anis le between vector p and the Z- asis, y is Angle 42 Scantee witan write CamScanner direction cosines

Oscanner Cosy = 9 Cosß = y gi Zosd 7. 8 Magnitude of p. rector "[2] B= Cos9 Cost 3 So, 2 = Cost our Now look into problem. = 30° given) O Alr, y, z) 30° 12m > B ON t y A X Figure In the given problemi - we find the Coordinates 3 Coordinates will be (ay, o) are going to A ( 311.87239 First In the Figure Coordinates of A is hage of we will find - which of A Vector on x-y plane

Yase IF cul look the deg IF we the look into diagram From alone like z - asis 1+ miu look y y 140° N Figure - 3 So А on is is component of Vector the gay plane. So, to A't = Sin30") -10A. LOAT = ş. 12=6 To Sin (30) Angle 30 is y, which? is Angle between z-asis and vector P Fon) - stagratitude of vector A] Anglor p e EŚ Scanneī wita Cos you cascanner y Cos 50

=) = 6 Cos you 6 Cos sou y = À will so Coordinate fetusuro', 660558) And IF Consider AN dereng In xyz to System then А" Glosyou, blosso", Al is in my plane Nous dook the - Figure we can find Alx, y, z) vector A. of point - Coordinate which is representing so Cos 30° 를 ОА A z=(Cos30°). 12 30/12 z = 12 cos30° z = 12.55 [: Cosso - do m] 2 cs Scanned with za CamScannert

So, Can Conclude How collectively ne coordinates of point A mil that be. (x, y, z) = ( 6 cos 40", 6 Cosso", 653) So Expressing A in terms of Cartesian Components A (vector 16 to 540 )i + (blosso) 9+ (653) Ř to Ary vector represents As. P (vector) = (ait yg +Z E 16 Now to find Find Angles between Vector and positive gray anises. As in Figure 1 ß = Costly Costa + 3 - Magnitude of giren vector here 8=104) AL t 6los you 12 m y = blosso CS Scanned with CamScanner

x-asis And between So, for recto A. Angle Los d = 1 To Dot product 70 LAI. los a = co (6 los 40 î + 6 Bassooit 653 R J 6205400+ 6² los 50 + 6² 43 Cost = folosyo 1 x2 6 Cosyo toto (36+ 3643 Cost Tosyo = 67.47 = for Angle between y-aris and Vector A. cos p= ĵ. ĵ. (bcos 4o î +60350 +63 19 IAI 36 +3643 Tosß=ot 6 Cosso to Cosso 6x2 > Ba Cosy Cossoo 71.25 2 Note or :-?. î = 1 & iij. to R, Jok zo 고 Cs. Scanged with x-axis asis Camo canner
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