Given two vectors: 3.3 +5.7 and b-423.8 What is the length of the component of v

Question

Given two vectors: 3.3 +5.7 and b-423.8 What is the length of the component of vector along the direction of vector b? The answer will be unitless D | Question 5 2 pts A vector t with components 7.5 +3.9 has a direction pointing into the first quadrant (both x and y components are positive). Find a vector of unit length that is perpendicular to the vector and is directed into the second quadrant (x component negative, y component positive) Enter the x-component of this vector into the answer box. Make sure the sign js correct. No new data to save. Last checked at 9:33am Submi ile. Do you want to clean it up for a fresh, like-new experience? And by the way, welcome back

Explanation / Answer

Suppose Vector d = -a i + b j

Now given that vector d is unit vector

|d| = 1, So

We also know that

|d| = sqrt ((-a)^2 + b^2) = 1

a^2 + b^2 = 1, So

Now also given that Vector d and Vector c are perpendicualr, So

d.c = 0

(-a i + b j).(7.5 i + 3.9 j) = 0

7.5*a - 3.9*b = 0

7.5*a = 3.9 b

b = (7.5/3.9)*a = 1.92*a

Now we also know that

a^2 + b^2 = 1

a^2 + (1.92*a)^2 = 1

a = sqrt [1/(1 + 1.92^2)]

a = 0.46

And

b = 1.92*a = 1.92*0.46 = 0.88

So Vector d will be

d = (-0.46) i + 0.88 j

x-component of d vector = -0.46

Please Upvote.

Comment below if you have any doubt.

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

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