Unit vector parallel to the resultant of vectors A⃗=4 î-3 ĵ and B⃗=8 î+8 ĵ will be (A) (24 î+5 ĵ

step 1 In this question we will learn about some basic concept of the vectors. The question is unit vec

Unit vector parallel to the resultant of vectors A⃗=4 î-3 ĵ...

Unit vector parallel to the resultant of vectors $\vec{A}=4 \hat{i}-3 \hat{j}$ and $\vec{B}=8 \hat{i}+8 \hat{j}$ will be
(A) $\frac{24 \hat{i}+5 \hat{j}}{13}$
(B) $\frac{12 \hat{i}+5 \hat{j}}{13}$
(C) $\frac{6 \hat{i}+5 \hat{j}}{13}$
(D) None of these

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Key Concepts

Vector Addition

Vector addition is the process of combining two or more vectors to produce a resultant vector. It involves adding the corresponding components of each vector, which is fundamental in understanding how different vector quantities interact in space.

Resultant Vector

The resultant vector is the single vector that has the same effect as performing the addition of multiple vectors. It is used to simplify the analysis of multiple forces or movements by combining them into one equivalent vector.

Magnitude of a Vector

The magnitude of a vector is a measure of its length or size in space. It is calculated using the square root of the sum of the squares of its components, and it is a crucial step when normalizing a vector to create a unit vector.

Unit Vector

A unit vector is a vector with a magnitude of one that indicates direction only. It is obtained by dividing a vector by its magnitude, which is known as normalization. Unit vectors play a vital role in representing directions without scaling effects.

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