Find a vector of magnitude 4 in the direction of the given vector y = 4i - 2k an

Question

Find a vector of magnitude 4 in the direction of the given vector y = 4i - 2k and a vector of magnitude 5 in the opposite direction of v. Find the angle between the two vectors Find proj_v u Find two vectors perpendicular to the plane containing u and v who are opposite to each other. u = 2i + 3k, v = 2i j + k u =2i + 3k, v = 3t - j - 2k Find the area of the parallelogram whose vertices are given: (1, 0, -1), (1, 7, 2), (2, 4, -1), (0, 3, 2) Find the parametric equation for the line through P(1, 2, -1) and Q(-1, 0, 1) Find the equation of the plane through (1, 1, -1), (2, 0, 2) and (0, 2, -1)

Explanation / Answer

(1) v = 4i - 2k

Magnitude of this vector is (4^2 + (-2)^2) = 20 = 25

A unit vector in the direction of v is (4i - 2k)/25

A vector of magnitude 4 in the direction of v is 4 *  (4i - 2k)/25 = (2/5)(4i - 2k)

A unit vector in the opposite direction of v is (-4i + 2k)/25

A vector of magnitude 5 in this direction is 5 * (-4i + 2k)/25 = (5 /2)(-4i + 2k).

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.