Let us define system of vectors u→1=v→1 and u→k=v→k−proju→1⁡v→k−…−proju→k−1⁡v→k,k≥2, where proja→⁡(b→)=(b→⋅a→)a→|a→|2 and v→1=2i^+j^−k^,v→2=i^+j^+k^,v→3=3i^−2j^−k^.Which of the following is INCORRECT?

u→2=v→2−proju→1⁡v→2Hence u→1⋅u→2=0u→3=v→3−proju→1⁡v→3−proju→2⁡v→3similarly u→3⋅u→1=0 and u→3⋅u→2=0

Let us define system of vectors u→1=v→1 and u→k=v→k−proju→1⁡v→k−…−proju→k−1⁡v→k,k≥2, where proja→⁡(b→)=(b→⋅a→)a→|a→|2 and v→1=2i^+j^−k^,v→2=i^+j^+k^,v→3=3i^−2j^−k^.Which of the following is INCORRECT?

u→2=v→2−proju→1⁡v→2Hence u→1⋅u→2=0u→3=v→3−proju→1⁡v→3−proju→2⁡v→3similarly u→3⋅u→1=0 and u→3⋅u→2=0

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Let us define system of vectors ${\vec{u}}_{1} = {\vec{v}}_{1}$ and ${\vec{u}}_{k} = {\vec{v}}_{k} - {proj}_{{\vec{u}}_{1}} ({\vec{v}}_{k}) - \dots - {proj}_{{\vec{u}}_{k - 1}} ({\vec{v}}_{k}), k \geq 2,$ where ${proj}_{\vec{a}} (\vec{b}) = \frac{(\vec{b} \cdot \vec{a}) \vec{a}}{| \vec{a} |^{2}}$ and ${\vec{v}}_{1} = 2 \hat{i} + \hat{j} - \hat{k}, {\vec{v}}_{2} = \hat{i} + \hat{j} + \hat{k}, {\vec{v}}_{3} = 3 \hat{i} - 2 \hat{j} - \hat{k}$ .
Which of the following is INCORRECT?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

${\vec{u}}_{2} \cdot {\vec{v}}_{1} \neq 0$

${\vec{u}}_{3} \cdot {\vec{v}}_{1} = 0$

$[{\vec{u}}_{1} {\vec{u}}_{2} {\vec{u}}_{3}] \neq 0$

${\vec{u}}_{3} \cdot {\vec{v}}_{2} \neq 0$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Question Image
${\vec{u}}_{2} = {\vec{v}}_{2} - {proj}_{{\vec{u}}_{1}} {\vec{v}}_{2}$
Hence ${\vec{u}}_{1} \cdot {\vec{u}}_{2} = 0$
${\vec{u}}_{3} = {\vec{v}}_{3} - {proj}_{{\vec{u}}_{1}} {\vec{v}}_{3} - {proj}_{{\vec{u}}_{2}} {\vec{v}}_{3}$
similarly ${\vec{u}}_{3} \cdot {\vec{u}}_{1} = 0 and {\vec{u}}_{3} \cdot {\vec{u}}_{2} = 0$