Question

If A-ai +0.5j +0.5K is unit vector, then value of
'a' would be
​

Answer 1

Answer:

1/√2

Explanation:

Since it is a unit vector, magnitude = 1

so, √a²+0.5²+0.5²=1

⇒a²+0.25+0.25=1

⇒a²+0.5=1

⇒a²=0.5=1/2

⇒a=1/√2

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Answer 2

Answer:

$\frac{1}{\sqrt2}$

Explanation:

We are given that  a vector A is a  unit vector

A=$-a\hat{i}+0.5\hat{j}+0.5\hat{k}$

We have to find the value of a.

We know that if a vector is unit vector then its magnitude will be 1.

A=$x\hat{i}+y\hat{j}+z\hat{k}$

$\mid A\mid=\sqrt{x^2+y^2+z^2$

Using the formula

$\mid A\mid =\sqrt{(-a)^2+(0.5)^2+(0.5)^2}$

$1=\sqrt{a^2+0.25=0.25}$

Squaring on both sides then, we get

$1=a^2+0.5$

$a^2=1-0.5=0.5=\frac{5}{10}=\frac{1}{2}$

$a=\pm\frac{1}{\sqrt2}$

Then, the value of a would be $\frac{1}{\sqrt2}$.

Therefore,Option 1 is true.

Answer:$\frac{1}{\sqrt2}$