Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Use the vectors to determine two dot products: u•v and u•w
u=9i-6j
v=-3i-2j
w=19i+15j

Use The Vectors To Determine Two Dot Products Uv And Uw U9i6j V3i2j W19i15j class=

Sagot :

LammettHash

A

Take the product of corresponding components, then take the total:

u • v = (9i - 6j) • (-3i - 2j) = 9 (-3) + (-6) (-2) = -15

u • w = (9i - 6j) • (19i + 15j) = 9 × 19 + (-6) 15 = 81

Alternatively, use the definition and algebraic properties of the dot product.

• For any vector x,

x • x = ||x||²

where ||x|| is the magnitude of x.

• i • i = j • j = k • k = 1

• i • j = j • k = k • i = 0

• For any scalar c and any two vectors x and y,

cx • y = x • cy = c (x • y)

• For any vectors x, y, and z,

(x + y) • z = z • (x + y) = x • z + y • z

Then the products you want are

u • v = (9i - 6j) • (-3i - 2j)

… = -27 (i • i) + 18 (j • i) - 18 (i • j) + 12 (j • j)

… = -27 + 12 = -15

u • w = (9i - 6j) • (19i + 15j)

… = 171 (i • i) - 114 (j • i) + 135 (i • j) - 90 (j • j)

… = 171 - 90 = 81

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.