Answer :
Answer:
Explanation:
a= 7.8i + 6.6j - 7.1k
b= -2.9 i+ 7.4 j+ 3.9k , and
c = 7.6i + 8.8j + 2.2k
r = a - b +c
=7.8i + 6.6j - 7.1k - ( -2.9i + 7.4j+ 3.9k )+ ( 7.6i + 8.8j + 2.2k)
= 7.8i + 6.6j - 7.1k +2.9i - 7.4j- 3.9k )+ 7.6i + 8.8j + 2.2k
= 18.3 i +18.3 j - k
the angle between r and the positive z axis.
cosθ = 18.3 / √18.3² +18.3² +1
the angle between r and the positive z axis.
= 18.3 / 25.75
cos θ= .71
45 degree
Vector product :
The vector product of any unit vector, i, j, or k, with itself is zero. The vector product of any one of these three unit vectors with any other one, however, is not zero because the included angle is not zero.
Given:
- a= 7.8i + 6.6j - 7.1k
- b=-2.9 i+ 7.4 j+ 3.9k
- c= 7.6i + 8.8j + 2.2k
Given condition: r = a - b +c
In order to calculate the value of r, we will substitute the values of a , b and c:
[tex]r=7.8i + 6.6j - 7.1k - ( -2.9i + 7.4j+ 3.9k )+ ( 7.6i + 8.8j + 2.2k)\\\\r= 7.8i + 6.6j - 7.1k +2.9i - 7.4j- 3.9k )+ 7.6i + 8.8j + 2.2k\\\\r= 18.3 i +18.3 j - k[/tex]
d)
The angle between r and the positive z axis.
[tex]cos\theta =\frac{18.3}{\sqrt{18.3^2+18.3^2 +1} }\\\\cos\theta = \frac{18.3}{25.75}\\\\cos\theta = 0.71\\\\\theta= 45^o[/tex]
e) The component along the direction of b will be:
[tex]=A cos \theta[/tex]
where the value of [tex]\theta=45^o[/tex]
f)
The magnitude of component of a perpendicular to the direction of b but in the plane of a and b.
b=-2.9 i+ 7.4 j+ 3.9k
[tex]|b|=\sqrt{(-2.9)^2+(7.4)^2+(3.9)^2} \\\\|b|=\sqrt{8.41+54.76+15.21}\\\\|b|=\sqrt{78.38} \\\\b=8.85[/tex]
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