Vector Calculus Answers

If U = I + 3j - 2k and V = 4i - 2j - 4k are vectors, find (2U + V) . ( U - 2V )
4
3
5
6
7 If
r4=r1+r2+r3
. Which of the vectors are linearly dependence on each .

r1

r3

r2

r4
8 A vector quantity has both magnitude and ----.
direction
time
magnitude
scalar
9 What does the symbol i,j,k denote
distance
velocity
unit vector
angle
10 Evaluate the vectors (2i - 3j).[(I +j - k) x (3i - k)]
7
4
6
2

What type of vector is w+(-w)=0
null vector
scalar vector
vector
magnitude
2 A scalar quantity has ---- only.
direction
magnitude
force
vector
3 Find the angle between U =4i - 2j + 4k and V = 3i - 6j - 2k .

680

670

580

690
4 A ..... is such that it can slide along its line of action.
vector
null vector
motion
line vector
5 If U = I + 3j - 2k and V = 4i - 2j - 4k are vectors, find 3U + V
10
14
4
11

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 A ...... line AB occurs when the point A is fixed.
free vector
position vector
force
null vector
9 A north-easterly wind of 20 knots is a ...... quantity.
scalar
weight
vector
distance
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 ...... is the sum of two vectors.
resultant vector
free vector
null vector
position vector
5 A temperature of
1000
C is a ...... quantity.
force
scalar
vector
magnitude

What are the component of a vector
I,x,k
I,j,k
y,x,i
w,I,k
7 If
r4=r1+r2+r3
,which of the vectors are linearly dependent .

r1

r3

r4

r2
8 Tf u.v=v.u,what does the law conotes;
associative
commutative
distributive
scalar
9 A dot product is said to be distributive,if ……..
m.u=u.m
m(u.v)=v(m.v)
u.(v+w)=(u.v+u.w)
m=u
10 Given that :
r−1=6i−8j+2k,r2=4i+5j+7k,r3=−2i+j+6kisavector.Findr1r2
30
26
-26
19

What does I,j denotes ………..
column
unit vector
scalar
matrix
2 Represesnt the given velocity 230km/h in the direction
2000
7cm
5cm
14cm
10cm
3 A negative vector could be denoted as ……….
w,w
a,b
u,v
u,-u
4 The sum of a vector and the negative of another vector could be written as …………
w+w
w+(-w)
w
None of the above
5What type of vector is w+(-w)=0
null vector
scalar vector
vector
magnitude

The differential coefficient of y = sin3x is ……….
3Cos 3x
3sin x
Cos(-3x)
cos 3x

b cos Q measures
the length of the projection of a on a line parallel to a.
the length of the projection of b on a line equal to b.
the length of the projection of b on a line parallel to b.
the length of the projection of a on a line equal to a.

Let a = 2i - j and b = i + j + k , evaluate a x b.
3k+2j-i
i +2j+3k
3k-2j-i
i+2j-3k

if angle between a vector and b vector be 30 degree , then if i want to find the perpendicular unit vector , then the new vector will be perpendicular to both a and b . how is it possible. in figure, if if angle between a vector and b vector be 30 degree, then the angle between a and the new vector be 90 and b and the new vector be 60 . then how the new vector will be perpendicular to both a and b? please explain me with figure.