9. The points A(2, -1, 0), B(1, 1, 1), C(3, 0, 1) and D(-(1)/(2), (1)/(2), (1)/(√(2))) are given

Step 1: Compute vector AB = B - A = (1-2, 1-(-1), 1-0) = (-1, 2, 1). Its magnitude |AB| = sqrt[(

Question

9. The points A(2, -1, 0), B(1, 1, 1), C(3, 0, 1) and $D\left(-\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}\right)$ are given. Which of the following statements are true? I. $|\vec{AB}| > |\vec{BC}|$ II. The position vector of A is parallel to the vector $\vec{u} = -2\vec{i} + \vec{j}$. III. The position vector of D is a unit vector. (a) I only (b) II only (c) I, II (d) II, III (e) I, II, III

          9. The points A(2, -1, 0), B(1, 1, 1), C(3, 0, 1) and $D\left(-\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}\right)$ are given. Which of the following statements are true?
I. $|\vec{AB}| > |\vec{BC}|$
II. The position vector of A is parallel to the vector $\vec{u} = -2\vec{i} + \vec{j}$.
III. The position vector of D is a unit vector.
(a) I only
(b) II only
(c) I, II
(d) II, III
(e) I, II, III

9. The points A(2, -1, 0), B(1, 1, 1), C(3, 0, 1) and D(-(1)/(2), (1)/(2), (1)/(√(2))) are given. Which of the following statements are true?
I. |A⃗B⃗| > |B⃗C⃗|
II. The position vector of A is parallel to the vector u⃗ = -2i⃗ + j⃗.
III. The position vector of D is a unit vector.
(a) I only
(b) II only
(c) I, II
(d) II, III
(e) I, II, III

Added by Nathan M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

10/03/2023

Step 1

Its magnitude |AB| = sqrt[(-1)^2 + 2^2 + 1^2] = sqrt(1 + 4 + 1) = sqrt(6). Show more…

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9. The points A(2,-1,0), B(1,1,1), C(3,0,1) and $$D\left(-\frac{1}{2},\frac{1}{2},\frac{1}{\sqrt{2}}\right)$$ are given. Which of the following statements are true? I. $$|\overrightarrow{AB}|>|\overrightarrow{BC}|$$ II. The position vector of A is parallel to the vector $$u=-2i+j$$. III. The position vector of D is a unit vector. (a) I only (b) II only (c) I, II (d) II, III (e) I, II, III