Given the vectors: a =-31-e, -=-1-1- Find the following: a) A vectorsuch that- +

Question

Given the vectors: a =-31-e, -=-1-1- Find the following: a) A vectorsuch that- + -o, b) A vector a such that 2 a 3Bo, c) the magnitude of a b.a g) c(a+ b) 7. A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30° east of north for 25 km. Draw the vector diagram and determine the total displacment of the car from the starting point. a horizontal right facing force of 70 Newtons, a downward directed force at an angle of 45° to left of 80 Newtons, and an upward directed force at an angle of 30° degree above the horizontal to the right of 60 Newtons 8. What is the resultant force produced by a vertical upward force of 50 Newtons,

Explanation / Answer

6a.

a = 4i - 3j + k

b = - i + j + 4k

when a - b + c = 0

c = b - a

c = (- i + j + 4k) - (4i - 3j + k)

c = - 5i + 4j + 3k

6b.

when 2a + 3b + d = 0

d = -(2a + 3b)

d = -(2*(4i - 3j + k) + 3*(- i + j + 4k))

d = -(8i - 6j + 2k - 3i + 3j + 12k)

d = -5i + 3j - 14k

6c.

a = 4i - 3j + k

|a| = sqrt (4^2 + (-3)^2 + 1^2)

|a| = sqrt 26 = 5.099

6d.

b = - i + j + 4k

|b| = sqrt ((-1)^2 + 1^2 + 4^2)

|b| = sqrt 18 = 4.24

6e.

a.b = (4i - 3j + k).(- i + j + 4k)

we know that in dot product

i.i = j.j = k.k = 1

&

i.j = j.k = k.i = i.k = j.i = k.j = 0

Using these

a.b = -4*(i.i) - 3*(j.j) + 4*(k.k)

a.b = -4 - 3 + 4 = -3

6f.

from dot products property

a.b = b.a

b.a = -3

6g

c.(a + b) = ?

a + b = (4i - 3j + k) + (-i + j + 4k)

a + b = 3i - 2j + 5k

c.(a + b) = (- 5i + 4j + 3k).(3i - 2j + 5k)

= -15*(i.i) - 8 (j.j) + 15*(k.k)

= -15 - 8 + 15

c.(a + b) = -8

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