A^→=3 +2 -5 k^∧ and B^→=++2 k^∧ Find |A^→+2 B^→| (A) √(40) (B) √(42) (C) √(39) (D) 2

Name: Problem 269, Chapter 2: JEE Physics
Uploaded: 2022-01-04T18:23:37-08:00
Duration: 3 min 9 s
Channel: Muhammad Nawaz
Description: A^→=3 +2 -5 k^∧ and B^→=++2 k^∧ Find |A^→+2 B^→| (A) √(40) (B) √(42) (C) √(39) (D) 2

step 1 Hello students our question is vector a is equal to 3 iK plus 2 jkf finance 5kkkk and vector b i

A^→=3 +2 -5 k^∧ and B^→=++2 k^∧ Find |A^→+2 B^→| (A) √(40)...

$ \mathrm{A}^{\rightarrow}=3 \hat{\imath}+2 \hat{\jmath}-5 \mathrm{k}^{\wedge}$ and $\mathrm{B}^{\rightarrow}=\hat{\imath}+\hat{\jmath}+2 \mathrm{k}^{\wedge}$ Find $\left|\mathrm{A}^{\rightarrow}+2 \mathrm{~B}^{\rightarrow}\right|$
(A) $\sqrt{40}$
(B) $\sqrt{42}$
(C) $\sqrt{39}$
(D) 2

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Key Concepts

Magnitude of a Vector

The magnitude of a vector represents its length or size and is calculated as the square root of the sum of the squares of its components. This concept is a cornerstone in vector analysis, providing a measure of how large the vector is irrespective of its direction, and is widely used in various fields such as physics, engineering, and computer graphics.

Vector Addition

Vector addition involves combining two or more vectors to produce a resultant vector. In a Cartesian coordinate system, this is done by adding corresponding components from each vector. This operation is fundamental in physics and engineering for analyzing cumulative effects of multiple vector quantities, such as forces or velocities.

Scalar Multiplication

Scalar multiplication is the process of multiplying a vector by a number (scalar), which scales the magnitude of the vector without changing its direction. This operation adjusts the length of the vector while preserving its directional properties, making it essential when coefficients or weights need to be applied to vector quantities.

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