Question

Find the magnitude of the vector A = 2i + 3j + 4k
a) 29
b) 9
c] √29
d] 13​

Answer 1

Answer:

1. UNCOUNTABLE NOUN

Science is the study of the nature and behaviour of natural things and the knowledge that we obtain about them.

The best discoveries in science are very simple.

...science and technology.

2. COUNTABLE NOUN

A science is a particular branch of science such as physics, chemistry, or biology.

Physics is the best example of a science which has developed strong, abstract theories.

...the science of microbiology.

Synonyms: discipline, body of knowledge, area of study, branch of knowledge More Synonyms of science

3. COUNTABLE NOUN

A science is the study of some aspect of human behaviour, for example sociology or anthropology.

...the modern science of psychology.

4. See also domestic science, exact science, Master of Science, political science, social science

Answer 2

$\\ \large✩ \rm \underline \pink{Question :- }$

★ Find the magnitude of the vector A = 2i + 3j + 4k

$\\ \large✩\rm \underline \pink{Solution :- }$

We know,

The magnitude of a 3d vector

$\\ \: \: \: \: \: \: \: \sf \: \: \: xi + yj + zk \: = \purple{\sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } }$

Therefore, the magnitude of a 3d vector, that is 2i + 3j + 4k is equal to

$\\ \: \: \: \: \: \: \: \sf \: \: = {\sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } }$

$\\ \: \: \: \: \: \: \: \sf \: \: = {\sqrt{ {(2)}^{2} + {(3)}^{2} + {(4)}^{2} } }$

$\\ \: \: \: \: \: \: \: \sf \: \: = {\sqrt{ 4+ 9 + 16 } }$

$\\ \: \: \: \: \: \: \: \sf \: \: = \color{green}{\sqrt{29} }$

Hence the magnitude of a 3d vector given,

$\\ \: \: \: \: \: \sf \: 2i + 3j + 4k = \underline{\sqrt{29} ≈5.38(approx)}$

So the option (c) is correct

$\\ \large✩ \rm \underline \pink{Note :- }$

The symbol ≈ denotes approximation.