In the above figure, vector
𝑥
_
has the same direction with what vectors?

Question

In the above figure, vector 
𝑥
_
 has the same direction with what vectors?

BlackTom AI · Accepted Answer

To begin, I will restate the problem and list the answer choices clearly so we can evaluate each option step by step.
Question: In the above figure, vector x has the same direction with what vectors?
Answer options: 
b, u.  
y, w.  
y, z.  
w, z.

Now, let's analyze each option in turn.
Option 1: b and u. Do vectors b and u point in the same direction as x? In the diagram, vector b appears to point in a steep upward-right direction similar to a diagonal. Vector u, however, is directed downward-right along a different slope than x. Since their directions do not coincide with x, this pair does not share the same direction as x, so this option is inconsistent with the requirement that x have the same direction as the other vectors.
Option 2: y and w. Here, vector y points to the right with a slight vertical component, while vector w is a long horizontal arrow to the left, which is opposite in direction to x or not aligned identically with x's orientation. The mismatch in direction between either y or w and x means this option cannot correctly describe vectors sharing the same direction as x.
Option 3: y and z. Vector y points to the right with a moderate upward tilt, and vector z points to the right along a similar horizontal line but at a different vertical level. Visually, both y and z align with the same general rightward direction as x, sharing the same sense of orientation along the horizontal axis. This makes them plausible candidates for having the same direction as x.
Option 4: w and z. While vector z does point to the right, vector w is directed leftward across a long span, which is opposite in direction to x. Therefore, w does not share the same direction as x, even though z might, the pair as a whole does not consistently match x's direction.

Based on directional alignment, we can compare each option against the direction of vector x. The option that includes vectors whose arrows point in the same orientation as x, without opposite or differing slants, is the one that satisfies the condition. In this analysis, the combination that matches x’s direction is y and z, because both vectors run to the right with a similar horizontal-oriented line as x. The other options mix directions that either oppose x (such as leftward) or diverge in slope, which fails the requirement of sharing the exact direction.

SMAT011 Week 1 Practice Quiz

In the above figure, vector 𝑥 _ has the same direction with what vectors?

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