Question

Let \(a\) and \(b\) be perpendicular vectors such that \(IaI=√104\) and \(IbI=6\).Then the value of\( Ia-bI\) is ?

• A. \(√110\)
• B. \(√140\)
• C. \(√98\)
• D. \(√55\)
• E. \(√70\)

Answer 1

The Correct Option is B

Step 1: Use the property of perpendicular vectors. Since \(\vec{a}\) and \(\vec{b}\) are perpendicular:
\[ \vec{a} \cdot \vec{b} = 0 \]

Step 2: Apply the formula for the magnitude of the difference of vectors:
\[ |\vec{a} - \vec{b}|^2 = |\vec{a}|^2 + |\vec{b}|^2 - 2(\vec{a} \cdot \vec{b}) \]
Given \(|\vec{a}| = \sqrt{104}\) and \(|\vec{b}| = 6\):
\[ |\vec{a} - \vec{b}|^2 = (\sqrt{104})^2 + 6^2 - 2(0) \]
\[ = 104 + 36 = 140 \]

Step 3: Take the square root to find the magnitude:
\[ |\vec{a} - \vec{b}| = \sqrt{140} \]

Conclusion: The value is \(\boxed{B}\) (\(\sqrt{140}\)).

Answer 2

Given 

Let \(a\) and \(b\) be perpendicular vectors such that;

 \(IaI=√104\) and \(IbI=6\).

We know that ,

\(|a-b|^{2}=|a|^{2}+|b|^{2}-2.|a|.|b|cos90°\)

\(⇒|a-b|^{2}=104+36-0\)

\(⇒|a-b|=√140\)