Ask Question
11 April, 06:41

Find the lengths of each of the following vectors

(a) 2i + 4j + 3k (b) 5i - 2j + k

(c) 2i - k (d) 5i

(e) 3i - 2j - k (f) i + j + k

+5
Answers (1)
  1. 11 April, 06:59
    0
    Generally, length of vector means the magnitude of the vector.

    So, given a vector

    R = a•i + b•j + c•k

    Then, it magnitude can be caused using

    |R| = √ (a²+b²+c²)

    So, applying this to each of the vector given.

    (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 means 1k

    The length is

    L = √ (5² + (-2) ²+1²)

    Note that, - * - = +

    L = √ (25+4+1)

    L = √30

    L = 5.477 unit

    (c) 2i - k

    Note that, since there is no component j implies that 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

    Same as above no is 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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Find the lengths of each of the following vectors (a) 2i + 4j + 3k (b) 5i - 2j + k (c) 2i - k (d) 5i (e) 3i - 2j - k (f) i + j + k ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers