MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Sum of Coefficients of All Terms

If a⃗,b⃗,c⃗...

Question

If $\to a, \to b, \to c$ and $\to d$ are unit vectors such that $(\to a \times \to b) \cdot (\to c \times d) = 1$ and $\to a \cdot \to c = \frac{1}{2}$ , then

A

\to a, \to b, \to c

are non-coplanar

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\to b, \to c, \to d

are non-coplanar

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\to b, \to d

are non-parallel

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

\to a, \to d

are parallel and

\to b, \to c

are parallel

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $\to b, \to d$ are non-parallel
$(\to a \times \to b) \cdot (\to c \times d) = 1$

$\Rightarrow (\to a . \to c) (\to b . \to d) - (\to a . \to d) (\to b . \to c) = 1$

$\Rightarrow \frac{1}{2} (\to b . \to d) - (\to a . \to d) (\to b . \to c) = 1$

$\Rightarrow \to b . \to d = 2 [1 - (\to a . \to d) (\to b . \to c)] \geq 0$ , since $a, b, c, d$ are unit vector
Hence $\to b, \to d$ are non-parallel.

Suggest Corrections

thumbs-up

0

Similar questions

\to b, \to c, \to d

are non-coplanar vectors, then the vector

(\to a \times \to b) \times (\to c \times \to d) + (\to a \times \to c) \times (\to d \times \to b) + (\to a \times \to d) \times (\to b \times \to c)

\to b, \to c, \to d

are non-coplanar vectors then the vector

(\to a \times \to b) \times (\to c \times \to d) + (\to a \times \to c) \times (\to d \times \to b) + (\to a \times \to d) \times (\to b \times \to c)

\to a, \to b, \to c, \to d

are non-coplanar vectors then the vector

(\to a \times \to b) \times (\to c \times \to d) + (\to a \times \to c) \times (\to d \times \to b) + (\to a \times \to d) \times (\to b \times \to c)

is parallel to:

If $\to a, \to b, \to c$ , and $\to d,$ are the unit vectors such that $(\to a \times \to b) . (\to c \times \to d) = 1$ and $\to a . \to c = \frac{1}{2},$ then

\to a, \to b, \to c

\to d

are unit vectors such that

(\to a \times \to b) . (\to c \times \to d) = λ

\to a . \to c = \frac{\sqrt{3}}{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Sum of Coefficients of All Terms

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Sum of Coefficients of All Terms

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon