Section A Question 1. a⃗ =3i+j ; b⃗ =2i+j+3k.

Section A
Question 1⃗
a=3i+j ; ⃗ b=2i+j+3k⃗
a .⃗ b= |a||b|cosƟ
7=√ 10∗ √ 14 cosƟ
Ɵ=cos−1
( 7
√ 140 )
=cos−1 ( .591607 )
=53.72880
Approximately = 540
Question 2
F1=15N in direction j
F2=XY N in the direction of i+2j+k
Where XY=86
F1=15j ; F2=86(i +2 j + k)
F1+F2=86 i+187 j+86 k
Magnitude of this resultant= √ 862 +1872 +862
=223.071N
That is approximately = 223.1N
Question 3⃗
a=3i+j⃗
b=2i+j+3k
Vector perpendicular to these two vectors is the cross product of the two vectors.
That is we have to find ⃗ a ×⃗ b,

=⃗a ×⃗ b=
|i j k
3 1 0
2 1 3|
=3i-9j+k
Unit vector = ⃗ a×⃗ b
|⃗a×⃗ b|
= 1
√91(3i-9j+k)
Section B
Question 4
W= sin 2t
cos 3 t
= dw
dt = 2cos 3tcos 2 t+3 sin 2 tsin 3t
( cos 3 t)2
Where t =86
= dw
dt at t=86
=.078217
Question 5
= y= ( x2 −5 )4
= dy
dx =4 (x2−5)3 2 x
d2 y
dx2 =48 x2 ¿
Question 6
∫
0
π
sin 3 t + 3
2 √ t dt