Question

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

Answer 1

Answer on Question #52234 – Math – Vector Calculus

1) What are the component of a vector

l,x,k

l,j,k

y,x,i

w,l,k

ANSWER:

l,j,k

7) If

r4=r1+r2+r3

, which of the vectors are linearly dependent.

r1

r3

r4

r2

ANSWER:

Def.

Vectors $a_1, a_2, \ldots, a_n$ are linearly dependent if there exist scalars (real numbers) $k_1, k_2, \ldots, k_n$, not all of which are zero, such that their linear combination

$$k_1 a_1 + k_2 a_2 + \cdots + k_n a_n = 0.$$

This problem deals with $r1+r2+r3- r4=0$

Vectors $a_1, a_2, \ldots, a_n$ are linearly independent if the equation

$$k_1 a_1 + k_2 a_2 + \cdots + k_n a_n = 0 \text{ can only be satisfied by } k_1 = 0, k_2 = 0, \ldots, k_n = 0.$$

Thus, vectors r1,r2, r3, r4 are linearly dependent.

8) If u.v=v.u, what does the law conotes;

associative

commutative

distributive

scalar

ANSWER:

commutative

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

ANSWER:

m·u=u·m - commutative

m(u·v)=v(m·v) - associative

u·(v+w)=(u·v+u·w) - distributive

m=u - scalar

10) Given that :

r1=6i-8j+2k,

r2=4i+5j+7k,

r3=-2i+j+6k is a vector.

Find r1r2

30

26

-26

19

ANSWER:

The dot product r1r2=6·4+(-8)·5+2·7=24-40+14=-2

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