Question 867363: I have no clue how to do these problems. Please help
Find the expression.
1.) u = (-3,-2), v = (-8, -11) Find u-v
choices: a.) (-5,-19) b.) (-1,3) c.) (5,9) d.) (-11,-13)
2.) w = (-1,3) and v = (0,1) Find ||-4w -v||
choices: a.) 185 b.)sqrt 185 c.) sqrt 155 d.) 155
3.) u = 4i - 6j and v = -5i - 21j; Find ||v-u||
choices: a.) sqrt 34 b.) -2 sqrt 34 c.) 3 sqrt 35 d.) 3 sqrt 34
4.) if v = 3i + j and w = -10i + j; Find ||v + w||
choices: a.) sqrt 130 b.) 13 c.) sqrt 53 d.) sqrt 111
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Find the expression.
1.) u = (-3,-2), v = (-8, -11) Find u-v
choices: a.) (-5,-19) b.) (-1,3) c.) (5,9) d.) (-11,-13)
Simply subtract the corresponding elements like so:
u - v = (-3,-2) - (-8, -11)
u - v = (-3-(-8),-2-(-11))
u - v = (-3+8,-2+11)
u - v = (5,9) which is choice C
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2.) w = (-1,3) and v = (0,1) Find ||-4w -v||
choices: a.) 185 b.)sqrt 185 c.) sqrt 155 d.) 155
First multiply everything in w by -4 to get
w = (-1,3)
-4w = -4(-1,3)
-4w = (-4(-1),-4(3))
-4w = (4,-12)
Then subtract off v
-4w - v = (4,-12) - (0,1)
-4w - v = (4-0,-12-1)
-4w - v = (4,-13)
Finally, find the length of this vector using the formula ||x|| = sqrt(a^2 + b^2) where x = (a,b)
So,
||-4w - v|| = sqrt((4)^2 + (-13)^2)
||-4w - v|| = sqrt(16+169)
||-4w - v|| = sqrt(185) which is choice B
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3.) u = 4i - 6j and v = -5i - 21j; Find ||v-u||
choices: a.) sqrt 34 b.) -2 sqrt 34 c.) 3 sqrt 35 d.) 3 sqrt 34
First compute v-u
v-u = (-5i - 21j) - (4i - 6j)
v-u = -5i - 21j - 4i + 6j
v-u = -9i - 15j
Then find the length of this vector
||v-u|| = sqrt((-9)^2+(-15)^2)
||v-u|| = sqrt(81+225)
||v-u|| = sqrt(306)
||v-u|| = sqrt(9*34)
||v-u|| = sqrt(9)*sqrt(34)
||v-u|| = 3*sqrt(34) which is choice D
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4.) if v = 3i + j and w = -10i + j; Find ||v + w||
choices: a.) sqrt 130 b.) 13 c.) sqrt 53 d.) sqrt 111
Start by adding vectors v and w
v + w = (3i+j) + (-10i+j)
v + w = 3i+j-10i+j
v + w = -7i+2j
Now compute the length
||v + w|| = sqrt(a^2 + b^2)
||v + w|| = sqrt((-7)^2 + (2)^2)
||v + w|| = sqrt(49+4)
||v + w|| = sqrt(53) which is choice C
Answer by josgarithmetic(39630) (Show Source):
You can put this solution on YOUR website! For number 1, you add or subtract components. Your question is "u-v" and you have the components of u and of v.
u-v=( -3-(-8), -2-(-11) )
( -3+8, -2+11 )
( 5, 9 ).
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