Vector Calculus Answers

Given that P = (-5, 11) and Q = (-6, 4), find the component form and magnitude of vector QP.

In a right angled triangle labelled ABC and C is 90degreea, which vector represents the resultant of the other two?

1)verify that the vector fields are conservation by conparing cross derivatives,then potential functions for the, by taking anti-derivatives
A)f=(z,1,x)
B)f=(y^(2),2xy+e^(z)+ye^(z))
C)f=(cosz,2y,-xsinz)

Calculate the divergence of the vector field f
A)f=(xy,yz,y^(2)-x^(3))
B)f=(x,y,z)
C)f=(x-2z(x^(2)),z-xy,(z^(2)x^(2))

For the following vectors
a = (2,3,5), b = (4,6,8), c = (-1,-5,9)
Calculate
a·(b × c)

For the following vectors
a = (3,5,7) and b = (4,6,8)
Calculate the following:
a) a × b
b) b × a

For the following vectors:
a = (1,-5,9), b = (-4,12,-6), c = (-3,5,-7)
Calculate the following:
a) a+b
b) b-c
c) 2a

For the following vectors:
a = (1,-5,9), b = (-4,12,-6), c = (-3,5,-7)
Calculate the following dot products:
a) a·b
b) a·c
c) b·c

What are vectors that are not parrallel to the same line,called.
scalar
collinear vectors
non-collinear vectors
vectors
7 Find the vector product axb. If a = 2i + 3j + 4k and b = 5i - 2j + k
11i + 18j - 19k
2j + 3k
5i - 6j + 7k
4i - 6j +11k
8 Find the scalar product a.b. If a = 2i + 3j + 4k and b = 5i - 2j + k
9
10
8
7
9 The centroid of a triangle of the triangle OAB is denoted by G. If o is the origin and line(OA) = 4i + 3j, line(OB) = 6i - j,find line(OG) in terms of the unit vectors I and j
10i - 3j

12(10i−2j)
10i + 2j

13(10i+2j)
10 Given that a = 5i +2j - k and b = I - 3j + k. Find (a + b) x (a + b).
2i - 12j - 34k
2i + 12j + 34k
2i -3j + 12j
2i + 2k

IF line(OA) =4i + 3j, line(OB) = 6i - 2j and line(OC) =2i - j . Deduce the length of the triangle CA.

13−−√

20−−√

29−−√

17−−√
2 What quantity have both magnitude and direction ?
vector
scalar
mass
dot product
3 Find the vector product axb. If a = i + 2j - k and b = 2i + 3j + k
5i - 3j - k
2i - 4j - k
3i + j - k
I - j + 3k
4 a and b are vectors defined by a = 8i + 2j - 3k and b = 3i - 6j + 4k, where I,j,k are mutually perpendicular unit vectors. Show that a and b are perpendicular to each other.
90
45
1
0
5 a and b are vectors defined by a = 8i + 2j - 3k and b = 3i - 6j + 4k, where I,j,k are mutually perpendicular unit vectors. Calculate a and b.
1
0
2
4