A^⟶=2 i ∧+2 j ∧-k ∧and B^→=2 i ∧-j ∧-2 k ∧Find 3 A^→-2 B^→ (A) 2 i ∧+7 j ∧+k ∧(B) 2 i ∧+8 j ∧-

step 1 Hello students our question is a is equal to 2i kp plus 2 jkap minus kk in b is equal to 2 i kk

A^⟶=2 i ∧+2 j ∧-k ∧and B^→=2 i ∧-j ∧-2 k ∧Find 3 A^→-2 B^→...

$\mathrm{A}^{\boldsymbol{\longrightarrow}}=2 \mathrm{i} \wedge+2 \mathrm{j} \wedge-\mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=2 \mathrm{i} \wedge-\mathrm{j} \wedge-2 \mathrm{k} \wedge$ Find $3 \mathrm{~A}^{\rightarrow}-2 \mathrm{~B}^{\rightarrow}$ (A) $2 \mathrm{i} \wedge+7 \mathrm{j} \wedge+\mathrm{k} \wedge$ (B) $2 \mathrm{i} \wedge+8 \mathrm{j} \wedge-\mathrm{k} \wedge$ (C) $2 \mathrm{i} \wedge+8 \mathrm{j} \wedge+\mathrm{k} \wedge$ (D) $\mathrm{i} \wedge+7 \mathrm{j} \wedge+\mathrm{k} \wedge$

$\mathrm{A}^{\boldsymbol{\longrightarrow}}=2 \mathrm{i} \wedge+2 \mathrm{j} \wedge-\mathrm{k} \wedge$ and $\mathrm{B}^{\rightarrow}=2 \mathrm{i} \wedge-\mathrm{j} \wedge-2 \mathrm{k} \wedge$ Find $3 \mathrm{~A}^{\rightarrow}-2 \mathrm{~B}^{\rightarrow}$
(A) $2 \mathrm{i} \wedge+7 \mathrm{j} \wedge+\mathrm{k} \wedge$
(B) $2 \mathrm{i} \wedge+8 \mathrm{j} \wedge-\mathrm{k} \wedge$
(C) $2 \mathrm{i} \wedge+8 \mathrm{j} \wedge+\mathrm{k} \wedge$
(D) $\mathrm{i} \wedge+7 \mathrm{j} \wedge+\mathrm{k} \wedge$

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Key Concepts

Vector Representation in Component Form

In three-dimensional space, vectors are typically expressed by decomposing them into their component parts along the x, y, and z axes using unit vectors (i, j, k). This representation allows for clear manipulation of each directional element independently.

Scalar Multiplication

This concept involves multiplying a vector by a scalar, which scales each component of the vector by that scalar value. The operation changes the vector's magnitude while its direction remains the same or reverses if the scalar is negative.

Vector Addition and Subtraction

Vector addition and subtraction are performed by combining corresponding components of the vectors. These operations are fundamental for calculating resultant vectors when dealing with multiple forces or directions.

Linear Combination of Vectors

A linear combination involves scaling one or more vectors by constants and then summing them up. This process is used to express a new vector in terms of others, and is a critical concept in vector spaces and linear algebra.

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