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

The value of α = 4√2Length 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 − 3kSo, length of a is |a| = √(5² + 4² + 0²) = √(25 + 16) = √41length of b is |b| = √(0² + α² + (-3)²) = √(α² + 9)Finding the value of αSince |a| = |b|√41 = √(α² + 9)Squaring both sides, we have41 = α² + 9α² = 41 - 9α² = 32 Taking square root of both sides, we haveα = √32α = √(16 × 2)α = 4√2So, the value of α = 4√2Learn more about length of a vector here: