MyQuestionIcon

1

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

Scalar Triple Product

If p= b× c ...

Question

If $p = \frac{b \times c}{[a b c]}, q = \frac{c \times a}{[a b c]}, r = \frac{a \times b}{[a b c]}$ where $a, b, c$ are three non-coplanar vectors then the value of the expression $(a + b + c) . (p + q + r)$ is

A

3

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

B

2

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

C

1

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

D

0

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

Open in App

Solution

The correct option is D 3
$a . p = \frac{a . (b \times c)}{[a b c]} = \frac{[a b c]}{[a b c]} = 1 = b . q = c . r$
$b . p = \frac{b . (b \times c)}{[a b c]} = \frac{0}{[a b c]} = 0 = c . q = a . r$
Therefore , the given expression is equal to
$(a + b + c) . (p + q + r) = 1 + 0 + 1 + 0 + 1 + 0 = 3$

Suggest Corrections

thumbs-up

0

Similar questions

\to a, \to b, \to c

are three non-coplanar vectors,

\to p, \to q, \to r

are non-zero vectors such that

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]},

then the value of the expression

(\to a + \to b + \to c), (\to p + \to q + \to r)

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

\to a, \to b

\to c

are three non-coplanar vectors, then the value of the expression

(\to a + \to b + \to c) \cdot (\to p + \to q + \to r)

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

\to a, \to b

\to c

are three non-coplanar vectors, then the value of the expression

(\to a + \to b + \to c) \cdot (\to p + \to q + \to r)

\to a, \to b, \to c

be three non-coplanar vector and

\to p, \to q, \to r

be vectors defined by the relations

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}, \to q = \frac{\to c \times \to a}{[\to a \to b \to c]}, \to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

then the value of the expression

(\to a + \to b) . \to p + (\to b + \to c) . \to q + (\to c + \to a) . \to r

a, b

c

be three non-coplanar vectors and let

p, q

r

be vectors defined by the relations

p = \frac{b \times c}{a b c}, q = \frac{c \times a}{a b c}

r = \frac{a \times b}{a b c}

Then the value of the expression

(a + b) . p + (b + c) . q + (c + a) . r

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Scalar Triple Product

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Scalar Triple Product

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon