u→,v→,w→ be such that |u→|$$=1$$,|v→|$$=2$$,|w→|$$=3$$ . If the projection of v→ along u→ is equal to that of w→ along and u→ and vectors v→,w→ are perpendicular to each other, then |u→−v→$$+w$$→| equals :

Question

u→,v→,w→ be such that |u→|$$=1$$,|v→|$$=2$$,|w→|$$=3$$ . If the projection of v→ along u→ is  equal to that of w→ along and u→ and vectors v→,w→ are perpendicular to each other,  then |u→−v→$$+w$$→| equals :

Infinity Learn · Accepted Answer

v→ ⋅ u∧  $$=$$  w→ ⋅ u∧ v→  ⊥  w→   ⇒       v→  ⋅w→   $$=$$  $$0$$ Now, $$__$$|u→−v→$$+w$$→|$$2=u$$→$$2+v$$→$$2+w$$→$$2$$−$$2u$$→⋅v→−$$2w$$→⋅v→$$+2u$$→⋅w→$$=1+4+9$$ So, $$__$$|u→−v→$$+w$$→|$$=14$$

$\vec{u}, \vec{v}, \vec{w} be such that | \vec{u} | = 1, | \vec{v} | = 2, | \vec{w} | = 3 . If the projection of \vec{v} along \vec{u} is$ $equal to that of \vec{w} along and \vec{u} and vectors \vec{v}, \vec{w} are perpendicular to each other,$ $then | \vec{u} - \vec{v} + \vec{w} | equals :$

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u→,v→,w→ be such that |u→|=1,|v→|=2,|w→|=3 . If the projection of v→ along u→ is equal to that of w→ along and u→ and vectors v→,w→ are perpendicular to each other, then |u→−v→+w→| equals :

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$\vec{u}, \vec{v}, \vec{w} be such that | \vec{u} | = 1, | \vec{v} | = 2, | \vec{w} | = 3 . If the projection of \vec{v} along \vec{u} is$ $equal to that of \vec{w} along and \vec{u} and vectors \vec{v}, \vec{w} are perpendicular to each other,$ $then | \vec{u} - \vec{v} + \vec{w} | equals :$