Ch-3

1
Ch-3

• Help-Session

2
CH-3-082

• T082 Q7. Vector A has a magnitude of 40.0 cm and
  is directed 60.0 degrees above the negative
  x-axis. Vector B has magnitude of 20.0 cm and is
  directed along the positive x-axis. Find the
  resultant vector (i and j are unit vectors along
  positive x and y axes, respectively). (Ans 34.6
  j cm)

• Q8. Consider two vectors
• A (3 i 4 j) cm and
• B (- 4 i 3 j) cm. Find the angle between
  these two vectors. (Ans 90 degrees)

A.B?A??B?cos? AxBxAyBy ? cos-1
(AxBxAyBy)/ ?A??B? ?A? ?B? 5 ? cos-1
(-1212)/ 25 cos-1(0) ? 90 degrees
CAB A ?A? cos 120 i ?A? sin 120 j A -
20.0 i 34.6 j B 20 i CAB (-2020) i
34.6 j 34.6 j
3
CH-3-082/081

• Q9. If vector A is added to vector B, the result
  is (6 i 1j) m. If A is subtracted from B, the
  result is (- 4 i 7 j) m. Find the magnitude of
  B. (Ans. 4 m.)

• T081 Q7. A boat travels a distance of 27.0 km
  20.0o North of East. It then travels 53.0 km in a
  direction 30.0o East of North. What is the total
  distance traveled by the boat in the East
  direction? ( Ans 51.9 km)

BA 6 i 1j B-A - 4 i 7 j Adding both
equations together 2B 2 i 8j Bi4j ?B?
?(1242) 4
?A? 27 km, ?A 20 ?B?53 km ?B60 CxAxBx
?A?cos 20 ?B? cos60 Cx25.37 26.5 51.9
4
CH-3-081

• Q8. Consider two vectors A and B with
  magnitudes 5 cm and 8 cm, respectively. Vector A
  is along the positive x-axis and vector B is
  along the positive y-axis. Find A? (AB). (Ans
  25 cm2)

• Q9. Consider the following three vectors A 5i
  2j-5k,
• B -2i4j3k, and Ci-2j-3k . Find the
  magnitude of the vector D A B 2C. (Ans
  17.7)

D A-2B3C 5i2j-5k2i-4j-3k2i-4j-6k
9i-6j-14k D ? (9262142 ) ? 313 17.7
A5i B8j AB 5i8j A. (AB) 5x5 25
5
CH-3-072

• T072 Q5.Vectors a, b, and c are related through
  equations and ABC A-B5C. If C 3i4j, what
  is the magnitude of vector a ? (Ans 15)

• Q6. Three vectors F,v and B are related through
  F 5(vxB) . If vector v3i -5j and B-2k, then
  vector F is (Ans 50 i30 j )

ABC A-B5C Adding both equations together
2A6C A3C A3C9i12j ?A ? ?(92122) 15
F 5(vxB)5(3i -5j)x(-2k) 5 -6i
xk10jxk)56j10i 30 j50 i
6
CH-3-072

• Q7. A vector A of magnitude 20 is added to a
  vector B of magnitude 25. The magnitude of the
  vector AB can be (Ans 12)

Q8. Vectors F and G are defined as F3i4j , and
G-ij . Find the component (projection) of
vector G along the direction of vector F .( Ans
0.20)
F.G?F??G?cos ? FxGxFyGy ?G?cos ?
(FxGxFyGy)/?F? (-34)/?(3242)1/5 0.2
?AB?max 252045 ?AB?min 25-20 5 Value of
?AB?5-45
7
CH-3-071
T071  In Fig. 3, the unknown vector C is given
by (AnsB-A )
Q8. Two vectors are given by
P-1.5i2j,and Q1.0j . The angle that the
vector makes with the positive x-axis is (A
135)
A-C B -CB-A CA-B
?cos-1(PxQxPyQy)/?P ? ? Q ? cos-1(2x1)/(??1.
5222) x1)
8
CH-3-071
Q5. Q9. A man walks 5.0 km due North, then 13 km
22.6 South of East, and then 12 km due West. The
man is finally at (Ans where he started)
Add components A5j B13 km 22.6 degrees south
of east C -12i Resultant must be Zero