a⃗, b⃗, c⃗ are three coplanar vectors. Find the vector sum. a⃗=4 î-ĵ, b⃗=-3 î+2 ĵ, c⃗=-3 ĵ (A) √

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

A⃗, b⃗, c⃗ are three coplanar vectors. Find the vector sum....

$\vec{a}, \vec{b}, \vec{c}$ are three coplanar vectors. Find the vector sum. $\vec{a}=4 \hat{i}-\hat{j}, \vec{b}=-3 \hat{i}+2 \hat{j}, \vec{c}=-3 \hat{j}$
(A) $\sqrt{5}, 297^{\circ}$
(B) $\sqrt{5}, 63^{\circ}$
(C) $\sqrt{3}, 297^{\circ}$
(D) $\sqrt{3}, 63^{\circ}$

Key Concepts

Vector Addition

Vector addition involves summing the corresponding components of vectors to obtain a resultant vector. This process is fundamental in determining the net effect when multiple vectors are combined, regardless of the forces or directions involved.

Component-wise Analysis

Component-wise computation is the technique where each vector is broken down into its individual components (usually along the i, j, and k unit vectors) and then these components are added together. This simplifies the process of vector addition by handling each dimension separately.

Vector Magnitude

The magnitude of a vector represents its length and is calculated using the square root of the sum of the squares of its components. This concept is crucial in determining the overall size of the vector regardless of its direction.

Direction Determination

Finding the direction of a vector involves calculating the angle it makes with a reference axis, typically using the inverse tangent function of the ratio of its y-component to its x-component. This method is essential in converting a vector from its component form to a polar form with both magnitude and angle.

Unit Vectors

Unit vectors, such as the i and j vectors, provide a standardized way to express direction in a coordinate system. They are vectors of unit length that represent the orientation of the coordinate axes and are used to build and decompose other vectors.

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