 # a=i+2j+3k,b=3i-j+2k find dot product and angle between two vectors?

9 years ago

When the two vectors are placed this way, the vectors form the angle q . ... The
scalar product (dot product) A · B (A dot B) of vectors A and B is the ... Given A = i
- j + k and B = 3i + 2j - k, find (a) A · B, (b) | A |, | B |, (c) the cosine of the angle
between A and ... Find the vector projection, Proj A B when A = 5j - 3k and B = i +
j + k.

9 years ago

a=i+2j+3k

b=3i-j+2k

we know that  i.i=1 , j.j=1 , k.k=1. and i.j=j.i=i.k=k.i=j.k=k.j=0.

a.b=3-2+6=7

a.b=abcosθ

cosθ=(a.b)÷ab

{a=√a.a, b=√b.b}  [ a=√14=b}

cosθ=7÷(14)=.5

θ=60

9 years ago

a.b = lal*lbl* cosx

and  i.i=k.k=j.j=1

and i.j=i.k=j.k=0

hence a.b=3-2+6=7

and lal*lbl=sqrt(14)*sqrt(14)=14

hence 7=14*cosx

cosx = .5

x=60degree

9 years ago

DOT PRODUCT OF TWO VECTORS:

a=i+2j+3k,b=3i-j+2k then a.b=(1)(3)+(2)(-1)+(3)(2)=3-2+6=7

let  alpha be the angle between the vectiors a and b. then cos(alpha)=a.b/modulus(a).modulus(b)

=7/root14.root14

=7/14=1/2

=cos(alpha)=cos60

=alpha=60

4 years ago
4-2+2=4 this way etfthnjjfdd hhfgj grdh ghbc will din run the yeah dude teach give you the yeah hung day going have fun of him he go get can go to if that's fine you is go is well ha well if so if so I'd will of do if so Kushagra Madhukar
askIITians Faculty 629 Points
2 years ago
Dear student,
Please find the solution to your problem.

a = i + 2j + 3k
|a| = √14
b = 3i – j + 2k
|b| = √14
Hence, a.b = 3 – 2 + 6 = 7
Let Q be the angle between them.
Hence, cosQ = a.b/|a||b| = 7/(√14 x √14)
= 7/14 = ½
or, cosQ = ½
Hence, Q = 60o

Thanks and regards,
Kushagra