Find α given that 5i+4j and αj−3k have the same length.

The value of α = 4√2

The length of a vector r = xi + yj + zk with x and y component and z components , x and y  and z is |r| = √(x² + y² + z²)

Let a = 5i + 4j and b = αj − 3k

So, length of a is |a| = √(5² + 4² + 0²)

= √(25 + 16)

= √41

length of b is |b| = √(0² + α² + (-3)²)

= √(α² + 9)

Since |a| = |b|

√41 = √(α² + 9)

Squaring both sides, we have

41 = α² + 9

α² = 41 - 9

α² = 32

Taking square root of both sides, we have

α = √32

α = √(16 × 2)

α = 4√2

So, the value of α = 4√2

Learn more about length of a vector here:

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answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

congruent segments

step-by-step explanation: