Use the alternative form of the dot product to find u · v.
||u||=45 , ||v||=30 and the angle between u and v is 5π/6.
(b) find the angle θ between the vectors in radians and in degrees.
u = cos( pi/3) i + sin(pi/3) j , v=cos (3pi/4)i + sin (3pi/4) j , find radians and degrees with respect to theta
c.) find the direction cosines and angles of u. notice that the sum of the squares of the direction cosines is 1. (round your answers for the angles to four decimal places.)
u = i + 4j + 8k
cos α, cos β, and cos γ,

Step-by-step explanation:

u = 45

v = 30

Angle between them, θ = 5π / 6 = 150°

(a) The formula for the dot product is given by

(b)

Let the angle between them is θ

The formula in terms of the dot product is given by

θ = 75°

(c)

f

step-by-step explanation:

f

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.