Free Printable E.M 1.4 Dot Product and Cross Product-1

1.

Determine the magnitude of the projection of the vector force F = 100N, onto u axis, from the figure given below.

a)

96.6 N

b)

60 N

c)

100 N

d)

70.7 N

2.

For two vectors $A$ and $B$ , what is $A,B$ (if they have angle α between them)?

a)

$|A||B|\cosα$

b)

$|A||B|$

c)

$\sqrt{√(|A||B|)}\cosα$

d)

$|A||B|\sinα$

3.

Which statement is right?

a)

Communitive law: $A\cdot B=B\cdot A$

b)

Multiplicative law: $a(A\cdot B)=A\times(aB)$

c)

Multiplicative law: $A\cdot(B+D)=(A\cdot B)+(A\cdot D)$

d)

Communitive law: $a(A\cdot B)=A\cdot(aB)$

4.

What is Distributive law?

a)

$A\cdot B=B\cdot A$

b)

$a(A\cdot B)=A\cdot(aB)$

c)

$A\cdot(B+D)=(A\cdot B)+(A\cdot D)$

d)

$a(A\cdot B)=A\times B$

5.

What is multiplication law?

a)

$A\cdot B=B\cdot A$

b)

$a(A\cdot B)=A\cdot(aB)$

c)

$A\cdot(B+D)=(A\cdot B)+(A.D)$

d)

$a(A\cdot B)=A\times B$

6.

Which is true for two vector
$A=A_1i+A_2j+A_3k$
and $B=B_1i+B_2j+B_3k\ ?$

a)

$A\cdot B=A_1B_1+A_2B_2+A_3B_3$

b)

$A\times B=A_1B_1+A_2B_2+A_3B_3$

c)

$A\cdot B=A_1B_2+A_2B_3+A_3B_1$

d)

$A\times B=A_1B_2+A_2B_3+A_3B_1$

7.

Determine the magnitude of the force F = 300j parallel to the direction of AB?

a)

155 N

b)

257.1 N

c)

200 N

d)

175 N

8.

What is

$k\cdot i\ ?$

a)

$0$

b)

$1$

c)

$-1$

d)

$\infty$

9.

What is $\left\{(i\cdot i)+(-i\cdot j)+(-k\cdot k)+(k\cdot i)\right\}\cdot(Ai+Bj+Cz)?$

a)

$1$

b)

$0$

c)

$A+B+C$

d)

$-1$

10.

. What is the range of $α$ ?

α=\cos^{-1}\left(\frac{A\cdot B}{AB}\right)

a)

$0˚<α<90˚$

b)

$0˚<α<180˚$

c)

$90˚<α<180C$

d)

$0˚<α<45˚$

11.

What is the value of $(A\times B)\cdot(C\cdot D)\times(A\times B)\cdot\left(C\cdot D\right)$ ?

For the four vectors $A,B,C$ and $D$ , with $A,B,C$ and $D$ all lying in the same plane?

a)

$i+j+k$

b)

$\sqrt{3\left(i+j+k\right)}$

c)

$0$

d)

$-1\left(i+j+k\right)$

12.

What is
$\left(A\times B)\cdot(B\times A\right)$ ; or

$A=A_1i+A_2j+A_3k$ and

$B=B_1i+B_2j+B_3k?$

a)

$0$

b)

$A_1B_1A_2B_2i+A_2B_2A_3B_3j+A_3B_3A_1B_1k$

c)

$A_1B_1A_1B_2i+A_2B_2A_3B_2j+A_3B_3A_1B_3k$

d)

$A_1B_1A_2B_1i+A_2B_2A_2B_3j+A_3B_3A_2B_1k$

13.

What is the value $\theta$ of in the figure given below?

a)

69˚

b)

60˚

c)

55˚

d)

90˚

14.

Refer to the diagram given , determine the magnitude of the force F = 300j perpendicular to the direction of AB.

a)

155N

b)

257.1N

c)

200N

d)

175N

15.

Determine the magnitude of the projection of the vector force F = 100N, onto the v axis, from the figure given .

a)

96.6N

b)

60N

c)

100N

d)

70.7N

E.M 1.4 Dot Product and Cross Product-1

Total questions: 15

Worksheet time: 45mins

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