Find the dot product vw w3j v4i O 5 O 0 7 12 SolutionSolutio

Find the dot product v·w. w=-3j v=-4i, O 5 O 0 -7 12

Solution:

(a) SInce we are dealing here with two coordinate vector i and j

Now let vecotor a = u i + v j and b = m i + n j

therefore dot product of two vector a and b is defined as

a.b = (u i + v j ) . (m i + n j ) = mu + vn

all reamaing part which are perpendicular to each other i and j term will be elminated because i.j = 0 . ( angle between and i and j is 90 )

therefore for this question v = -4i = -4i + 0j

w = -3j = 0i -3j

hence dot product of v and w = v.w = (-4i + 0j ) . (0i -3j) = 0

v.w = 0

Answer: 0

(b) Given that v = 9i + 5j

answer; w = (3/2)i +(5/6) j

explanation

v = 9i + 5j =

by taking 6 outside from RHS

v = 6 ( (3/2)i +(5/6) j )

v = 6 w

Hence It is parallel