(a) 6 𝐢+12 𝐣 (b) 𝐢+8 𝐣 (c) 3 𝐢 (d) √(65) (e) 3

Name: Problem 1, Chapter 7: Advanced Engineering Mathematics
Uploaded: 2021-08-22T17:10:51-08:00
Duration: 5 min 28 s
Channel: Gaurav Kalra
Description: (a) 6 𝐢+12 𝐣 (b) 𝐢+8 𝐣 (c) 3 𝐢 (d) √(65) (e) 3

Key Concepts

Vector Representation in Component Form

This concept refers to expressing vectors using their components along the coordinate axes, typically using unit vectors such as i and j in two dimensions. This allows the vector to be fully described by its horizontal and vertical components, which can then be used in various operations such as addition, subtraction, and scaling.

Magnitude of a Vector

The magnitude (or length) of a vector is a scalar value representing the distance from the origin to the point described by the vector. It can be computed using the Pythagorean theorem when the vector is represented in component form, by taking the square root of the sum of the squares of its components.

Scalar and Vector Quantities

This key concept distinguishes between scalars, which have only magnitude, and vectors, which have both magnitude and direction. Recognizing this difference is crucial when dealing with operations and properties that are exclusive to either type of quantity.

Transcript

00:01 Hi, we need to evaluate this way we have 4 root negative 8 plus 8 root 3 aorta.

00:10 It is the fourth root of this unit value to the 4th root of this unit value.

00:17 So first to find out it's a square root that's coming up to be we have root of the root of negative 8 plus 8 root 3 aorta.

00:29 So mostly find square root of this square root of negative 8 plus 8 root 3 aorta.

00:37 Let's evaluate this.

00:44 So now how to evaluate this? we just take here, negative 8 plus 8 root 3 iota equals we have a plus iota b square.

00:53 I'm going to find out a plus iota b here.

00:56 A plus iota b will note of this.

00:58 So all this now, negative 8 plus 8 root 3 iota.

01:02 That equals we have a square, negative b square plus 2b a b aorta.

01:08 A square negative b square, the real part, negative 8 and then 2ab equals.

01:13 Equals a root 3.

01:17 So we have ab is 4 root 3 here we have and a equals 4 root 3 over b.

01:27 So we are now here 4 root 3 over b whole square negative b equals negative a.

01:35 We will now keep on simplifying this.

01:40 We keep on following this here.

01:44 We just find out here the square root here.

01:47 So we got the values here we have and we get this equation here.

01:51 Just like widic formula.

01:54 In the quadratic formula we get b squared is 12 or a negative number, negative number i'm rejected here.

01:59 B is a real value.

02:00 It is positive.

02:01 So b is coming out of 2, a is plus minus 2.

02:05 So root b is coming out to be plus minus 2 plus aorta, 2 root.

02:11 So taken here this is coming up to be.

02:15 So this is taken as we have here, this coming out to be root c here we have.

02:24 So this part here we have.

02:31 This is root t...

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