Question

If A vector = 2i cap +4j cap - 5k cap . find the direction of cosines of the vector A​.​

Answer 1

Answer:

vector a is a giant si it is wrong question

Answer 2

Question :

If A Vector is

$\: \: \: \: \tt \vec{A} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}.$

Find the direction of Cosine of the Vector A.

AnsWer :

$\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \frac{2}{ 3\sqrt{5} } \: , \: \frac{4}{3 \sqrt{5} } \: , \: \frac{ - 5}{4 \sqrt{5} } .$

Formula Use :

$\red \star \: \tt \vec{A} = magnitude.direction.\\ \tt \red \star \: \vec{A} = |A| . \hat{A}. \\ \tt \red \star \: \hat{A} = \frac{ \vec{A}}{ |A| } .$

Calculation :

$\: \: \: \: \tt\vec{A} = 2 \hat{i} + 4 \hat{j} - 5 \hat{k}.$

$\leadsto \tt \hat{A} = \frac{ \vec{A}}{ |A| } \\ \leadsto \tt \hat{A} = \frac{ 2 \hat{i} + 4 \hat{j} - 5 \hat{k}}{ \sqrt{ {2}^{2} + {4}^{2} + { (- 5)}^{2} } }$

$\leadsto \tt \hat{A} = \frac{ 2 \hat{i} + 4 \hat{j} - 5 \hat{k}}{ \sqrt{45}} \\ \leadsto \tt \hat{A} = \frac{ 2 \hat{i} + 4 \hat{j} - 5 \hat{k}}{ 3\sqrt{5}}$

Now,

Coefficient of Cosine is,

$\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \frac{2}{ 3\sqrt{5} } \: , \: \frac{4}{3 \sqrt{5} } \: , \: \frac{ - 5}{4 \sqrt{5} } .$

Therefore, the direction of Cosine for Vector A is,

$\tt \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \frac{2}{ 3\sqrt{5} } \: ,\: \frac{4}{3 \sqrt{5} } \: , \: \frac{ - 5}{4 \sqrt{5} } .$