Advertisements
Advertisements
प्रश्न
Find \[\left| \vec{a} - \vec{b} \right|\] if
\[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 5 \text{ and } \vec{a} \cdot \vec{b} = 8\]
योग
Advertisements
उत्तर
\[\text { Given that }\]
\[\left| \vec{a} \right| = 2, \left| \vec{b} \right| = 5 \text{ and } \vec{a} . \vec{b} = 8 . . . \left( 1 \right)\]
\[\text{ We know that }\]
\[ \left| \vec{a} - \vec{b} \right|^2 = \left| \vec{a} \right|^2 + \left| \vec{b} \right|^2 - 2 \vec{a} . \vec{b} \]
\[ = 2^2 + 5^2 - 2 \left( 8 \right)............. \left[ \text{ Using } \left( 1 \right) \right]\]
\[ = 4 + 25 - 16\]
\[ = 13\]
\[ \therefore \left| \vec{a} - \vec{b} \right| = \sqrt{13}\]
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
