Question

If a unit vector is represented by 0.5 i + 0.8 j + ck then find the missing c

Answer 1

|a+b+c|=1
√0.5²+0.8²+c²=1
squaring both sides 
0.5²+0.8²+c²=1
0.25+0.64+c²=1
c²+0.89=1.00
c²=0.11
c=√0.11

Answer 2

Answer:

The ‘value of c’ is $\bold{\sqrt{0.11}}$ for the given unit vector.

Explanation:

Given:  

A ‘unit vector’ is represented by $0.5 \mathrm{i}+0.8 \mathrm{j}+\mathrm{ck}$

Solution:

We have been given a unit vector which is represented as $0.5 \mathrm{i}+0.8 \mathrm{j}+\mathrm{ck}$. A vector has ‘magnitude of one’.  

Hence, we can say that  $|a+b+c|=1$ $\sqrt{0.5}^{2}+\sqrt{0.8}^{2}+\sqrt{c}^{2}=1$

Squaring both sides  

$(0.5)^{2}+(0.8)^{2}+(c)^{2}=1$$0.25+0.64+c^{2}=1$$c^{2}+0.89=1.00$$c^{2}=0.11$$\bold{c=\sqrt{0.11}}$