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a_sh-v
3 months ago
6

Find the lengths of each of the following vectors

Physics
1 answer:
serg [3.5K]3 months ago
3 0

Answer:

Explanation:

The length of a vector refers to its magnitude.

For a vector

R = a•i + b•j + c•k

The magnitude can be calculated using

|R|= √(a²+b²+c²)

Applying this formula to each given vector yields the following results.

(a) 2i + 4j + 3k

The length is

L = √(2²+4²+3²)

L = √(4+16+9)

L = √29

L = 5.385 unit

(b) 5i − 2j + k

Note that k represents 1k

The length is

L = √(5²+(-2)²+1²)

Because, -×- = +

L = √(25+4+1)

L = √30

L = 5.477 unit

(c) 2i − k

As there is no j component, it means that the j component is 0

L = 2i + 0j - 1k

The length is

L = √(2²+0²+(-1)²)

L = √(4+0+1)

L = √5

L = 2.236 unit

(d) 5i

Similarly, without a j-component and k-component

L = 5i + 0j + 0k

The length is

L = √(5²+0²+0²)

L = √(25+0+0)

L = √25

L = 5 unit

(e) 3i − 2j − k

The length is

L = √(3²+(-2)²+(-1)²)

L = √(9+4+1)

L = √14

L = 3.742 unit

(f) i + j + k

The length is

L = √(1²+1²+1²)

L = √(1+1+1)

L = √3

L = 1.7321 unit

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