Magnitude of the resultant vector _________ What direction is the resultant vect

Question

Magnitude of the resultant vector
_________

What direction is the resultant vector pointing in?

It has no magnitude so the direction is irrelevant.
Due east (along the positive x-axis)
Due north (along the positive y-axis)
Due west (along the negative x-axis)
Due south (along the negative y-axis)
A northeasterly direction (first quadrant)
A northwesterly direction (second quadrant)
A southwesterly direction (third quadrant)
A southeasterly direction (fourth quadrant)
.
What is the angle between the resultant vector and the horizontal? If the magnitude of the resultant is zero, then enter 'none'.
_________°

Vector A has a magnitude of 41 and is pointing at an angle a=61 degree east of north. Vector B has a magnitude of 27 and is pointing at an angle b=72 degree south of west. Find the magnitude and direction of A+B (the sum of two vectors is more commonly known as the resultant vector). Magnitude of the resultant vector _________ What direction is the resultant vector pointing in? It has no magnitude so the direction is irrelevant. Due east (along the positive x-axis) Due north (along the positive y-axis) Due west (along the negative x-axis) Due south (along the negative y-axis) A northeasterly direction (first quadrant) A northwesterly direction (second quadrant) A southwesterly direction (third quadrant) A southeasterly direction (fourth quadrant). What is the angle between the resultant vector and the horizontal? If the magnitude of the resultant is zero, then enter 'none'. _________degree

Explanation / Answer

magnitude of vector A = 41 angle A = 61 degrees
vector A = 41 sin 61 i + 41 cos 61 j                = 35.85 i + 19.87 j where i , j are the unit vectors along east and north directions respectively magnitude of vector B = 27 angle B= 72 degrees vector B = 27 cos 72 *(-i) + 27 sin 72 *(-j)               = -27 cos 71 i -27 sin 72 j               = - 8.79 i -25.67 j resultant vector A+B = 35.85 i + 19.87 j - 8.79 i -25.67 j                                   = 27.06 i -5.8 j resulatant vector is in 4 th quadrant i.e., southeasterly direction (fourth quadrant)
magnitude of A+B is = [27.06^2 +(-5.8)^ 2]                                 = 27.67 units let the resulatnt makes an angle with east along south direction then tan = 5.8 / 27.06                 = 0.2143               = 12.09 degrees

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

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