3
1
VECTOR 8. SUBTRACTION OF VECTORS Vector which is want to subtracted just change direction of that vector and then add. ) B ( A B A → → → → - + = - EXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORS EXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORS EXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORS EXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORS EXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORS Ex.1 Given k ˆ j ˆ 2 i ˆ 3 a - + = → and k ˆ 3 j ˆ i ˆ b + + = → Determine (i) → → + b a (ii) → → - b a Sol. (i) ) k ˆ j ˆ 2 i ˆ 3 ( b a - + = + → → + ) k ˆ 3 j ˆ i ˆ ( + + (ii) ) k ˆ 3 j ˆ i ˆ ( ) k ˆ j ˆ 2 i ˆ 3 ( b a + + - - + = - → → k ˆ 3 j ˆ i ˆ k ˆ j ˆ 2 i ˆ 3 + + + - + = k ˆ 3 j ˆ i ˆ k ˆ j ˆ 2 i ˆ 3 - - - - + = k ˆ 2 j ˆ 3 i ˆ 4 + + = = k ˆ 4 j ˆ i ˆ 2 - + 9. PARALLELOGRAM LAW OF VECTOR To determine magnitude & direction of resultant vector, when two vectors act at an angle θ. According to this law if two vectors → P and → Q are represented by two adjacent sides of a parallelogram both pointing outwards as shown in fig. The diagonal drawn through the intersection of the two vectors represents the resultant → R . → → → + = Q P R From triangle OCM OC 2 = OM 2 + CM 2 = (P + Q cosθ) 2 + (Q sin θ) 2 = P 2 + Q 2 cos 2 θ + 2PQ cos θ + Q 2 sin 2 θ Since Q 2 (cos 2 θ + sin 2 θ) = Q 2 R 2 = P 2 + Q 2 + 2PQ cos θ θ + + = cos PQ 2 Q P R 2 2 (Magnitude of resultant vector) and tanφ = OM CM = θ + θ cos Q P sin Q or θ + θ = φ - cos Q P sin Q tan 1 (Angle of resultant vector with P)
-
Upload
pkgargiitkgp -
Category
Documents
-
view
212 -
download
0
description
kmnnm
Transcript of 3
-
VECTOR
8 . SUBTRACTION OF VECTORS
Vector which is want to subtracted just change direction of that vector and then add. )B(ABA
+=
EXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORSEXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORSEXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORSEXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORSEXAMPLE BASED ON ADDITION & SUBTRACTION OF VECTORS
Ex.1 Given kj2i3a +=
and k3jib ++=
Determine (i) + ba (ii)
ba
Sol. (i) )kj2i3(ba +=+
+ )k3ji( ++ (ii) )k3ji()kj2i3(ba +++=
k3jikj2i3 ++++= k3jikj2i3 +=
k2j3i4 ++= = k4ji2 +
9 . PARALLELOGRAM LAW OF VECTOR
To determine magnitude & direction of resultant vector, when two vectors act at an angle .
According to this law if two vectors
P and
Q are represented by two adjacent sides of a parallelogramboth pointing outwards as shown in fig. The diagonal drawn through the intersection of the two vectors
represents the resultant R .
+= QPR
From triangle OCM
OC2 = OM2 + CM2
= (P + Q cos)2 + (Q sin )2
= P2 + Q2 cos2 + 2PQ cos + Q2 sin2
Since Q2 (cos2 + sin2) = Q2
R2 = P2 + Q2 + 2PQ cos
++= cosPQ2QPR 22 (Magnitude of resultant vector)
and tan = OMCM
= +
cosQPsinQ
or
+
= cosQP
sinQtan 1 (Angle of resultant vector with P)
