Phys101
Term: 122
Online HW-Ch03-Lec02
Q1:
Vector A has magnitude L/2 and vector B has magnitude L/2. When drawn with their
tails at the same point, the angle between them is 60o. The magnitude of the vector
cross product A×B is:
A.
B.
C.
D.
E.
L
L2/4
0.87 L2/4
L2/8
none of these
Ans:
𝐂 ; ��A⃗ × �B⃗� = ABsin60 =
L
L √3
L2
L2
× ×
= 0.866
= 0.87
2
2
2
4
4
Q2:
What is the angle (in degrees) between the two vectors A = (3i + 2j) and B = (-2i +j
+2k)? (Give your answer in three significant figures form)
Ans:
�⃗. B
�⃗ = AB cosθ
A
⇒ (3 ı̂ + 2 ȷ̂). �− 2 ı̂ + ȷ̂ + 2 k� � = � �32 + 22 � � �22 + 12 + 22 � cosθ
⇒ (−6 + 2) = √13 √9 cosθ
−4
⇒ θ = cos −1 �
� = 112°
3√13
Q3:
Three vectors are given as: A= (3i + 2k), B = (-i - j + 2k) and C = (j +k). The value of
A.(B×C) is: (Give your answer in three significant figures form)
Ans:
ı̂
ȷ̂ k�
�
⃗
�
⃗
First: B × C = �−1 −1 2� = ı̂(−1 − 2) − ȷ̂(−1) + k� (−1) = −3ı̂ + ȷ̂ − k�
0
1 1
�⃗ × �⃗
Now ∶ �A⃗ . � B
C� = �3 ı̂ + 2 k� �. �−3ı̂ + ȷ̂ − k� �
= (3)(−3) + (2)(−1) = −9 − 2 = −11.0
KFUPM-Physics Department
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