Find the indicated quantity, assuming that u = 7i + j, v = i − 3j, and w = 3i+2j.     u · (v + w)

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A: See attached file for a step by step explanation to find the required quantity.

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Q: Find the indicated quantity, assuming that u = 7i + j, v = i − 3j, and w = 3i + 5j. u · (v + w)

A: First, we calculate v+w ,then take dot product with u .

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A: Given v=3i+j+3k, w=i-k

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Q: Find the indicated quantity, assuming u = 7i + j, v = i - 3j, and w = 3i + 5j. (u + v) · (u – v)

A: Givenu=7i+jv=i-3ju+v=7i+j+i-3j=8i-2ju-v=7i+j-(i-3j)=7i+j-i+3j=6i+4j

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A: For solution see step 2.

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Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2u + 3v (b) |u| (c) u-v…

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A: We know,  i·i=1 ; i·j=0 ; i·k=0j.i=0 ; j·j=1 ; j·k=0k.i=0 ; k·j=0 ; k·k=1

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A: u=11-4,  v=5-21,  w=01-3 . 2u+3v=211-4+35-21 2u+3v=22-8+15-63 2u+3v=17-4-5 2u+3v=17i-4j-5k

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Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2и + 3v (b) |u| (c) u-v…

A: Given vectors - u = i+j-2kv = 3i-2j+kw = j-5kPart (a) - 2u+3v = 2i+j-2k+33i-2j+k2u+3v =…

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