Let $\vec{a} = 4 \hat{i} + 5 \hat{j} - \hat{k}, \vec{b} = \hat{i} - 4 \hat{j} + 5 \hat{k}$ and $\vec{c} = 3 \hat{i} + \hat{j} - \hat{k}$ . Find a vector $\vec{d}$ which perpendicular to both $\vec{c} and \vec{b} and \vec{d} . \vec{a} = 21$

Solution

Since $\vec{d}$ is perpendicular to both $\vec{c}$ and $\vec{b}$ , therefore, if is parallel to $\vec{c} x \vec{b}$

$∴ \vec{d} = λ (\vec{c} x \vec{b}) = λ |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 1 & - 1 \\ 1 & - 4 & 5 \end{matrix}| = λ \{(5 - 4) \hat{i} - (15 + 1) \hat{j} + (- 12 - 1) \hat{k}\} = λ \{\hat{i} - 16 \hat{j} - 13 \hat{k}\} Given that \vec{d} . \vec{a} = 21 λ \{\hat{i} - 16 \hat{j} - 13 \hat{k}\} . (4 \hat{i} + 5 \hat{j} - \hat{k}) = 21 λ (4 - 80 + 13) = 21 λ = \frac{21}{- 63} = - \frac{1}{3} ∴ \vec{d} = \frac{1}{3} (\hat{i} - 16 \hat{j} - 13 \hat{k}) = (- \frac{1}{3}) \hat{i} + (\frac{16}{3}) \hat{j} + (\frac{13}{3}) \hat{k}$

Some More Questions From Vector Algebra Chapter

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Let $\vec{a} = 4 \hat{i} + 5 \hat{j} - \hat{k}, \vec{b} = \hat{i} - 4 \hat{j} + 5 \hat{k}$ and $\vec{c} = 3 \hat{i} + \hat{j} - \hat{k}$ . Find a vector $\vec{d}$ which perpendicular to both $\vec{c} and \vec{b} and \vec{d} . \vec{a} = 21$

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10^–19 coulomb

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

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Vector Algebra

Let a→ = 4i^ + 5j^ - k^ , b→ = i^ - 4j^ + 5k^ and c→ = 3i^ + j^- k^. Find a vector d→ which perpendicular to both c→ and b→ and d→. a→ = 21

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.2 meters north-west

Classify the following measures as scalars and vectors.40°

Classify the following measures as scalars and vectors.40 watt

Classify the following measures as scalars and vectors.10–19 coulomb

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 $\vec{a} = 4 \hat{i} + 5 \hat{j} - \hat{k}, \vec{b} = \hat{i} - 4 \hat{j} + 5 \hat{k}$ and $\vec{c} = 3 \hat{i} + \hat{j} - \hat{k}$ . Find a vector $\vec{d}$ which perpendicular to both $\vec{c} and \vec{b} and \vec{d} . \vec{a} = 21$

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10^–19 coulomb

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