The value of α = 4√2
Length of a vector
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)
Finding the value of α
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
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