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1 answer:
Answer:
b)0, yes
Step-by-step explanation:
Given:
Vectors (4,8) . (6,-3)
Finding inner product of vectors:
= 4x6 + 8x-3
=24-24
=0
Now to check the angle between them using formula a.b=|a|.|b|cosθ
|a|=
=8.9
|b|=
=6.7
Putting values of a.b=0 and |a|=8.9, |b|=6.7 in a.b=|a|.|b|cosθ we get,
0= 8.9(6.7)cosθ
cosθ =0
θ=90 degrees
Hence the two vectors are perpendicular !
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Answer:
x = 1/2
Step-by-step explanation:
The sum of numbers in all rows, columns and diagonals have to be the same.
Notice the diagonals do not have an x so let's sum those numbers to see what the sum for all must be.
-2+(1/2) +3 = (-4+1+6)/2 = 3/2
-5+(1/2)+6 = (-10+1+12)/2 = 3/2
Now we can pick the first row and sum the numbers up knowing that the result should be 3/2, will find x
-2+x-3+6 = 3/2, combine like terms
x+1 = 3/2 , subtract 1 from both sides
x = (3/2)-1, find common denominator and subtract
x = (3-2)/2, combine like terms
x = 1/2
Check or work:
Rows from top to down
-2 +(1/2) -3 +6 = (-4+1-6+12)/2 = 3/2✅
17*(1/2) +(1/2) +(1/2)-8 = (17+1+1-16)/2 = 3/2✅
-5+(9/2) -2(1/2) +3 = (-10+9-2+6)/2 = 3/2✅
Columns from left to right
-2+17(1/2)-5 = (-4+17-10)/2 =3/2✅
(1/2)-3+(1/2)+(9/2)-2(1/2) = (1-6+1+9-2)/2 = 3/2✅
6+(1/2)-8+3 = (12+1-16+6)/2 = 3/2✅
Diagonals
-2+(1/2) +3 = (-4+1+6)/2 = 3/2✅
-5+(1/2)+6 = (-10+1+12)/2 = 3/2✅
Step-by-step explanation:
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