Step1 oft A
No, (i +j+ I?) is not a unit vector.
By the definition, a unit vector is a vector of unit magnitude or a vector whose magnitude is 1. It is
unitless and dimensionless vector. It represents only directions in space.
Prove it as,
In Cartesian co
Step1 of3 A
(A) From this theory, we have lmi = 5280feet and lhout=36008
A speed of 60 miles per hour is
= 6036280 fb's
3600
Comment
Step 2 of 3 A
(B) The acceleration due to gravity is it/2?.2 .
From this theory, we have l=30.480m
We know that lm=100c1
Step1 of1 A
The formula to find the sum of two vectors A and B is:
R = A2 + .15?2 +2ABcosG
Here, R is the magnitude of resultant vector and a be the angle between two vectors A and B.
Assume A and B are the two pulls whose magnitudes are equal.
Let x be t
Step 1 of 1 h
d
If i=0 foravector in the (33;)ptane A=A ?+A 3
I J'
A, = -A,.
|A = ,/A,2 + A:
A + A; = 0
2 _ 2
A, _ A,
From Eulers rule r' is the imaginary unit
A:=:( :)
A):
Comment Step1 of3 A
Supposeleheighxofthepiletohideherh=200cm
Longthofthc pilehoh
Step 4 of 4 A
(C)
The vector 6' = C1? + Cy] is given as follows:
C =(A,F+ A,)+(Bj+ Bj)
fo+Cj =(A, + B,)f+(A,. + 3,
Substitute 7.oofor Bx, 2,00for By, -3,00for A1, and 5.00for A),
cj +03 = (3.00+ 7.00)? +(6.00+ 2.00) j-
= 4.00: + 8.00]
The angle of the vec
Step4of5 A
(B)
A = 5 unit
I! ' 4 unit
C = 6 unit
Comment
Step 5 of 5 A
Now,
A: (5c0526)z+(55m26)1+0k
=4 Si+2. 2J+0k
B = (4cos63)i+(4sin63)j+0k
=1. 8i+3. 6j+0k
c =0;+0j+6k >(1)
Now,
4.5 2.2
(Shaft: 1.3 3.6
o o
=4.5(3.6x6-0)+22(0-6xl.8) Step1 of1 A
The po
Step 3 of 3 A
(b)
The value of radius of the Earth is "e = 6.37 x l 03 km
Compute the ratio of radius of the new planet and the ratio of radius of the Earth to write
the radius of the new planet in terms of radius of the Earth.
R _ 1.641210" km
rE H 6.37:
Step1 ON A
Assumethemassofaperson= 70kg
The human body is mostly water.
The mass ofa water molecule =18.015u (here u' means atomicmass unit)
However, lu =l_6613<I1027 kg
The mass ofthe water molecule = 18.015uxl.661>~<10'27 1(qu
= 2.99x10' kg
Number of wa
Step 2 of 3 A
EXECUTE:
Gimmmempmduaofz and 3' vectorsisZ-=-6.0
Andthevectorptoductofxi and E vectorsis Zx=+9.o
Latheanglebetween .4' and B bee.
From the denition of scalar product of vectors 1 and? , wehave
Z-B=ABcosl9 . (1)
From the denition of vector pt