Let $\vec{u}$ be a vector coplanar with the vectors a $\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} a n d \vec{b} = \hat{j} + \hat{k} .$ $i f \vec{u} i s p e r p e n d i c u l a r t o \vec{a} a n d \vec{u} . \vec{b} = 24, t h e n | \vec{u} | i s e q u a l t o :$

84

336

315

256

Solution

336

$[\vec{u} . \vec{a} . \vec{b}] = 0 \Rightarrow \vec{u} = x \vec{a} + y \vec{b} \vec{u} . \vec{a} = 0 \Rightarrow x a^{2} + y \vec{a} . \vec{b} = 0 \vec{u} . \vec{b} = 24 x \vec{a} \vec{b} + y b^{2} = 24 (14 x 2 y = 0) - (2 x + 2 y = 24) = 12 x = - 24 x = - 2 y = 14 \vec{u} = - 2 \vec{a} + 14 \vec{b} \vec{u} = - 4 \hat{i} + 8 \hat{j} + 15 \hat{k} \Rightarrow | \vec{u} | = \sqrt{4^{2} + 8^{2} + 16^{2}} \Rightarrow | \vec{u} | = \sqrt{336} \Rightarrow | \vec{u} |^{2} = 336$

Some More Questions From Vector Algebra Chapter

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Vector Algebra

Let $\vec{u}$ be a vector coplanar with the vectors a $\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} a n d \vec{b} = \hat{j} + \hat{k} .$ $i f \vec{u} i s p e r p e n d i c u l a r t o \vec{a} a n d \vec{u} . \vec{b} = 24, t h e n | \vec{u} | i s e q u a l t o :$

84

336

315

256

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done

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Vector Algebra

Let u→ be a vector coplanar with the vectors a a→ = 2i^ + 3j^ -k^ and b→ = j^ +k^. if u→ is perpendicular to a→ and u→.b→ = 24, then |u→| is equal to: 84 336 315 256

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.20 m/s2

Classify the following measures as scalars and vectors.time period

Classify the following measures as scalars and vectors.distance

Classify the following measures as scalars and vectors.force

Classify the following measures as scalars and vectors.velocity

Classify the following measures as scalars and vectors.work done

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Let $\vec{u}$ be a vector coplanar with the vectors a $\vec{a} = 2 \hat{i} + 3 \hat{j} - \hat{k} a n d \vec{b} = \hat{j} + \hat{k} .$ $i f \vec{u} i s p e r p e n d i c u l a r t o \vec{a} a n d \vec{u} . \vec{b} = 24, t h e n | \vec{u} | i s e q u a l t o :$

84

336

315

256

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done