Two vectors p and q are given by:
p = 2i + j - K
q = i - 3j + 2k
Find:
a) p + q
b) Modulus (p + q)
c) Modulus (p) + Modulus (q)
d) (p) x (q)
a) p + q = (2i + j - k) + (i - 3j + 2k)
= 2i + 1j - 1k + 1i - 3j +2k
= i(2+1) + j(1-3) + k(-1+2)
= i(3) + j(-2) + k(1)
= 3i - 2j + 1k
= 3i -2j + k (Ans)
b) Modulus (p+q) = [ (3)2 + (-2)2 + (1)2 ]1/2
= [ 9 + 4 + 1]1/2
= [14]1/2
= 3.7416 (Ans)
c) Modulus (p) + Modulus (q) = [ (2)2 + (1)2 + (-1)2]1/2 + [ (1)2 + (-3)2 + (2)2]1/2
= [ 4 + 1 + 1]1/2 + [ 1 + 9 + 4]1/2
= [6]1/2 + [14]1/2
= 2.4495 + 3.7416
= 6.1911 (Ans)
d) Before we move into multiplication, some things to remember,
i * i = 0, i * j = 1k, i * k = -1j, j*i = -1k, j * j = 0, j * k = 1i, k*i = 1j, k * j = -1i, k*k = 0
(p) * (q) = (2i + j -k) * (i - 3j + 2k)
= 2i * (i - 3j + 2k) + j * (i - 3j +2k) - k * (i - 3j +2k)
= (2 * i * i )+ (2 * -3 * i * j) + (2 * 2 * i * k) + ( j * i) + ( 1 * - 3 * j * j) + ( 1 * 2 * j * k) + ( -1 * 1 * k * i) + (-1 * -3 * k * j) + (-1*2 * k * k)
= (2 * 0) + ( -6 * 1k) + ( 4 * -1j ) + (-1k) + ( -3 * 0 ) + ( 2 * 1i) + ( -1 * 1j) + ( 3 * -1i) + ( -2 * 0)
= (-6k) + ( -4j) + (-1k) + (2i) + (-1j) + (-3i)
= -6k - 4j -k + 2i -j -3i
= -6k -k - 4j -j +2i - 3i
= -7k - 5j -1i
= -1i -5j - 7k (Ans)
Given the following two vectors: A=2i+6j=3k and B=5i-3j-2k. Find the dot product of the two vectors, the cross product of the two vectors,a nd the angle between them.
HOMEWORK No. 4 1) If P, Q and S are vector forces and If P --2i+ 3j-4k and P Q=-i-j+kand S -3j MFI a) Find P.Q P -2 3-4 Q= 2X-D 311)+eD P.Q=-5 1 b) Find PX Q J K -2 3 -4 -1-1 1 fxQ=(5-)i +(-2-0j+(2-DK PxQ=-i-uj +5K c) Find Angle 31COS0 IG-N122 EN3 d) Unit Vector Q e) Find (P x Q).S (-i-aita = 13 f) Provide a graphical interpretation of the quantity (Px Q) . S g)...
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