Consider a in the positive direction of x, b in the positive direction of y, and

Question

Consider a in the positive direction of x, b in the positive direction of y, and a scalar d. What is the direction of b/d if d is (a) positive and (b) negative? What is the magnitude of (c) a middot b and (d) a middot b/d? What is the direction of the vector resulting from (e) a times b and (f) b times a? (g) What is the magnitude of the vector product in (e)? (h) What is the magnitude of the vector product in (f)? What are (i) the magnitude and (j) the direction of a times b/d if d is positive?

Explanation / Answer

Given two vectors a and b are in the directions

a is along +x direction , b is along +ve y direction, and a scalar d

a) the direction of 'b' if d is +ve is Along +ve y direction ,

b) the direction of 'b' if d is -ve is Along -ve y direction ,

c) the scalar or dot product of vectors is

a.b = ab cos theta , where theta is the angle between the vectors here theta= 90 degrees so

a.b = 0

d) magnnitude of a.b/d = a*b/d cos theta = a.b/d cos90 = 0

e) a X b = a*b sin theta = a*b sin 90 = a*b

f) b X a = - a X b = - a*b

g) magnitude of the vector product of a,b is simply the product of the magnitude of the vectors

h) magnitude of the vector product of b,a is simply the product of the magnitude of the vectors = -a*b

i) if d is positive the magnitude of a X b/d is = a*b/d sin90 = a*b/d

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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