Question

10. Magnitude of the given vector A = 57+ 67 - 3k is-
(a) 8
(b) 14
(c) 70
(d) root 70
please fast ​

Answer 1

Answer: Option(d) : √70

Vector :-

• A = 5i + 6j - 3k

Now, we have to find the magnitude of this vector. We know a vector is represented by two quantities i.e., Magnitude and direction.

For a vector,

⇒ A = |A| û

Where,

• |A| = Magnitude of vector A
• û = Direction of vector A
• A = vector

For a vector in vector-resolution form, its magnitude can be given by the square root of the sum of the squares of its i,k,k coefficients. (Coefficients of i, j and k)

So, here,

⇒ |A| = √{ (5)² + (6)² + (-3)² }

⇒ |A| = √( 25 + 36 + 9 )

⇒ |A| = √(70)

Hence, the magnitude of the given vector is √70, therefore Option (d) is correct.

Some Information :-

The sum of Vectors expressed in vector resolution form is given by the vector of whose i,j,k coefficients will be equal to the each respective coefficients of i,j,k.

For example,

• A = Aₓi + Aᵧj + A₂k
• B = Bₓi + Bᵧj + B₂k

So, the sum of vector is given by,

⇒ A + B = (Aₓ + Bₓ)i + (Aᵧ + Bᵧ)j + (A₂ + B₂)k

The same process is used to find the substraction, multiplication of vectors by subtracting, multiplying corresponding i,j,k coefficients of each vector.

Answer 2

Required answer:-

Question:

10. Magnitude of the given vector A = 57+ 67 - 3k is-

(a) 8

(b) 14

(c) 70

(d) root 70

Solution:

Given,

• A = 57 + 67 - 3k

To find:

• Magnitude of the given vector

As we know:

• A = |A| û

and

A is vector

|A| is magnitude of the vector A

û is direction of vector A

After taking the coefficients (i,j,k).....

Step by step explaination:

Now,

|A| = √{(5)² + (6)² + (-3)²}

|A| = √(25 +36 + 9)

$|A| \: = √70$

Answer:

Magnitude of the given vector A = 57+ 67 - 3k is

√70