Determine that vector which when added to the resultant of A⃗=3 î-5 ĵ+7 k̂ and B⃗=2 î+4 ĵ-3 k̂ g

step 1 In this question, we will learn about some basic concept of the vectors. The question is, when a

Determine that vector which when added to the resultant of...

Determine that vector which when added to the resultant of $\vec{A}=3 \hat{i}-5 \hat{j}+7 \hat{k}$ and $\vec{B}=2 \hat{i}+4 \hat{j}-3 \hat{k}$ gives a unit vector along the $y$-direction. (A) $5 \hat{i}+2 \hat{j}-4 \hat{k}$ (B) $-5 \hat{i}+2 \hat{j}-4 \hat{k}$ (C) $5 \hat{i}-2 \hat{j}-4 \hat{k}$ (D) None of these

Determine that vector which when added to the resultant of $\vec{A}=3 \hat{i}-5 \hat{j}+7 \hat{k}$ and $\vec{B}=2 \hat{i}+4 \hat{j}-3 \hat{k}$ gives a
unit vector along the $y$-direction.
(A) $5 \hat{i}+2 \hat{j}-4 \hat{k}$
(B) $-5 \hat{i}+2 \hat{j}-4 \hat{k}$
(C) $5 \hat{i}-2 \hat{j}-4 \hat{k}$
(D) None of these

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Key Concepts

Vector Addition

This concept involves adding two or more vectors by summing their corresponding components. It provides a method for combining individual forces or directions into a single resultant vector, which is essential in many areas of physics and engineering.

Unit Vectors

A unit vector has a magnitude of one and is used to indicate direction. They are often used to represent standard directional lines in coordinate systems, such as the x, y, or z axes, ensuring that only directional, not magnitude, information is conveyed.

Component-wise Operations

Operating on vectors component-wise means performing arithmetic operations independently on each of the vector's components. This method simplifies the process of solving vector equations by allowing the comparison and solution of corresponding components individually.

Solving Vector Equations

This entails using inverse operations to determine an unknown vector that, when added to a known vector (or vector sum), results in a desired outcome. It often involves working component by component to ensure that the equation holds true in each dimension.

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