Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 34

HARD

VITEEE

IMPORTANT

Earn 100

If the vertices of any tetrahedron be $\vec{a} = \hat{j} + 2 \hat{k}, \vec{b} = 3 \hat{i} + \hat{k}, \vec{c} = 4 \hat{i} + 3 \hat{j} + 6 \hat{k}$ and $\vec{d} = 2 \hat{i} + 3 \hat{j} + 2 \hat{k}$ then find its volume

50% studentsanswered this correctly

Important Questions on Vector Algebra

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 36

If

\vec{a}, \vec{b}, \vec{c}

are three non-coplanar non-zero vectors and

\vec{r}

is any vector in space, then

(\vec{a} \times \vec{b}) \times (\vec{r} \times \vec{c}) + (\vec{b} \times \vec{c}) \times (\vec{r} \times \vec{a}) + (\vec{c} \times \vec{a}) \times (\vec{r} \times \vec{b})

is equal to

MEDIUM

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 37

The moment about the point

\hat{i} + 2 \hat{j} + 3 \hat{k}

of a force represented by

\hat{i} + \hat{j} + \hat{k}

acting through the point

2 \hat{i} + 3 \hat{j} + \hat{k}

is

HARD

VITEEE

IMPORTANT

Comprehensive Guide to VITEEE Mathematics. Other applicable Exams - JEE Main, BITSAT, SRM JEE, MHT-CET, K-CET, EAMCET, AMU & Other State Engg. Entrance Exams>Chapter 15 - Vector Algebra>Exercise 2>Q 38

Let the unit vectors

\vec{a}

and

\vec{b}

be perpendicular to each other and the unit vector

\vec{c}

be inclined at an angle

θ

to both

\vec{a}

and

\vec{b}

. If

\vec{c} = x \vec{a} + y \vec{b} + z (\vec{a} \times \vec{b})

, then