Two perpendicular vectors are given in terms of their components by U equals Ux i - 4 j + 6 k and V equals 3 i + 2 j - 3 k. Determine the component Ux.

Two perpendicular vectors are given in terms of their components by U equals Ux i - 4 j + 6 k and V equals 3 i + 2 j - 3 k. Determine the component Ux.

• A. 5.67
• B. 6.67
• C. 7.67
• D. 8.67

Answer: (D)

When two vectors are perpendicular, their dot product is zero. So set U · V = 0. U = <Ux, -4, 6>, V = <3, 2, -3>. The dot product is Ux*3 + (-4)*2 + 6*(-3) = 3Ux - 8 - 18 = 3Ux - 26. Set this to zero: 3Ux - 26 = 0, giving Ux = 26/3 ≈ 8.666..., which is 8.67.

When two vectors are perpendicular, their dot product is zero. So set U · V = 0.

U = <Ux, -4, 6>, V = <3, 2, -3>. The dot product is

Ux*3 + (-4)2 + 6(-3) = 3Ux - 8 - 18 = 3Ux - 26.

Set this to zero: 3Ux - 26 = 0, giving Ux = 26/3 ≈ 8.666..., which is 8.67.