Ask question

Ask question

All categories

3 years ago

8

5. The analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions,

for which graphical work is inconvenient. Find the magnitude of the resultant of the vectors A = i12 —j37 + k58 and B = i5 + j30 — k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively

1 answer:

Gwar [14]3 years ago

6 0

Answer:

C = 17 i^ - 7 j^ + 16 k^ , | C| = 24.37

Explanation:

To work the vactor component method, we add the sum in each axis

C = A + B = (Aₓ + Bₓ) i ^ + ( $A_{y}$ + $B_{y}$ ) i ^ + ( $A_{z}$ + $B_{z}$ ) k ^

Cₓ = 12+ 5 = 17

$C_{y}$ = -37 +30 = -7

$C_{z}$ = 58 -42 = 16

Resulting vector

C = 17 i ^ - 7j ^ + 16k ^

The mangitude of the vector is

| C | = √ c²

| C | = √( 17² + 7² + 16²)

| C| = 24.37

You might be interested in

A straight segment of a current-carrying wire has a current element IL where I = 2.70 A and L = 3.20 cm i + 4.30 cm j. The segme

myrzilka [38]

The component of the force in negative z-direction is -0.144 N.

The given parameters;

<em>current in the wire, I = 2.7 A</em>
<em>length of the wire, L = (3.2 i + 4.3j) cm</em>
<em>magnetic filed, B = 1.24 i</em>

The force on the segment of the wire is calculated as follows;

$F = ILBsin(\theta)$

where;

<em>θ is the angle wire and magnetic field</em>

<em />

The force on the wire segment will be perpendicular in negative z-direction (applying right hand rule), so there won't be any x and y component of the force.

The angle between the wire and the magnetic field is calculated as follows;

$\theta = tan^{-1} (\frac{y}{x} )\\\\\theta = tan^{-1} (\frac{4.3}{3.2} )\\\\\theta = 53.3 \ ^0$

The magnitude of the wire length is calculated as follows;

$|l | = \sqrt{3.2^2 + 4.3^2} = 5.36 \ cm = 0.0536 \ m$

The component of the force in negative z-direction is calculated as;

$F_z = -ILB sin(\theta)\\\\F_z = -2.7 \times 0.0536 \times 1.24 \times sin(53.3)\\\\F_z = -0.144 \ N$

Thus, the component of the force in negative z-direction is -0.144 N.

Learn more here:brainly.com/question/22719779

6 0

2 years ago

PLEASE HELP ITS DUE IN 12 MINUTES

GrogVix [38]

A. Bones provide protection for organs in the body

5 0

2 years ago

A large bottle contains a number of medicinal tablets is 0.5kg. Calculate the number of tablets in the bottle?

Alexeev081 [22]

Answer:

the answer is 5k in the bottle have

8 0

3 years ago

With a 900 V source, voltage is divided across 3 series resistors of 300 V, 280 V, and:

telo118 [61]

Answer:

AAAAAAAAaaaaaaaaaaaaaaaaaaaaaaaaaaaa

6 0

2 years ago

A parallel-plate capacitor has square plates that are 8.00cm on each side and 4.20mm apart. The space between the plates is comp

Sergeu [11.5K]

Answer:

$U=1.29\times 10^{-7}\ J$

Explanation:

Given that

a= 8 cm (square)

A= a ² = 64 cm²

d= 4.2 mm

d₁= 2.1 mm ,K₁= 4.7

d₂=2.1 mm , K₂=2.6

We know that capacitance given as

$C_1=\dfrac{K_1\varepsilon _oA}{d_1}$

$C_1=\dfrac{4.7\times 8.85\times 10^{-12}\times 64\times 10^{-4}}{2.1\times 10^{-3}}$

$C_1=1.26\times 10^{-10}\ F$

$C_2=\dfrac{K_2\varepsilon _oA}{d_2}$

$C_2=\dfrac{2.6\times 8.85\times 10^{-12}\times 64\times 10^{-4}}{2.1\times 10^{-3}}$

$C_2=0.701\times 10^{-10}\ F$

Net capacitance

$C=\dfrac{C_1C_2}{C_1+C_2}$

$C=\dfrac{1.26\times 10^{-10}\times 0.701\times 10^{-10}}{1.26\times 10^{-10}+0.701\times 10^{-10}}\ F$

$C=4.5\times 10^{-11}\ F$

We know that stored energy given as

$U=\dfrac{CV^2}{2}$

V= 76 V

$U=\dfrac{4.5\times 10^{-11}\times 76^2}{2}\ J$

$U=1.29\times 10^{-7}\ J$

3 0

2 years ago