CameraIcon

SearchIcon

MyQuestionIcon

167

You visited us 167 times! Enjoying our articles? Unlock Full Access!

Selecting Consecutive Terms in A.P

The value of ...

Question

The value of $[\vec{a} - \vec{b}, \vec{b} - \vec{c}, \vec{c} - \vec{a}], where |\vec{a}| = 1, |\vec{b}| = 5, |\vec{c}| = 3, is$
(a) 0
(b) 1
(c) 6
(d) none of these

Open in App

Solution

(a) 0

$We have [\vec{a} - \vec{b}, \vec{b} - \vec{c}, \vec{c} - \vec{a}] = ((\vec{a} - \vec{b}) \times (\vec{b} - \vec{c})) . (\vec{c} - \vec{a}) (By definition of scalar triple product) = ((\vec{a} - \vec{b}) \times \vec{b} - (\vec{a} - \vec{b}) \times \vec{c}) . (\vec{c} - \vec{a}) = (\vec{a} \times \vec{b} - \vec{b} \times \vec{b} - \vec{a} \times \vec{c} + \vec{b} \times \vec{c}) . (\vec{c} - \vec{a}) = (\vec{a} \times \vec{b} - 0 - \vec{a} \times \vec{c} + \vec{b} \times \vec{c}) . (\vec{c} - \vec{a}) = (\vec{a} \times \vec{b}) . (\vec{c} - \vec{a}) - (\vec{a} \times \vec{c}) . (\vec{c} - \vec{a}) + (\vec{b} \times \vec{c}) . (\vec{c} - \vec{a}) = (\vec{a} \times \vec{b}) . \vec{c} - (\vec{a} \times \vec{b}) . \vec{a} - (\vec{a} \times \vec{c}) . \vec{c} + (\vec{a} \times \vec{c}) . \vec{a} + (\vec{b} \times \vec{c}) . \vec{c} - (\vec{b} \times \vec{c}) . \vec{a} = [\vec{a} \vec{b} \vec{c}] - [\vec{a} \vec{b} \vec{a}] - [\vec{a} \vec{c} \vec{c}] + [\vec{a} \vec{c} \vec{a}] + [\vec{b} \vec{c} \vec{c}] - [\vec{b} \vec{c} \vec{a}] = [\vec{a} \vec{b} \vec{c}] - 0 - 0 + 0 + 0 - [\vec{a} \vec{b} \vec{c}] (∵ [\vec{a} \vec{b} \vec{c}] = [\vec{b} \vec{c} \vec{a}] = [\vec{c} \vec{a} \vec{b}]) = 0$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The value of

[\to a - \to b \to b - \to c \to c - \to a]

| \to a | = 1, | \to b | = 5, | \to c | = 3

Q. The value of

[\to a - \to b \to b - \to c \to c - \to a]

| \to a | = 1, | \to b | = 5, | \to c | = 3

x = l o g_{b} a, y = l o g_{c} b, z = l o g_{a} c

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

are three vectors such that

\vec{a} + \vec{b} + \vec{c} = \vec{0} and |\vec{a}| = 2, |\vec{b}| = 3, |\vec{c}| = 5,

then the value of

\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \cdot \vec{c} \cdot \vec{a} is

(a) 0
(b) 1
(c) -19
(d) 38

Q. Consider a, b, c as real numbers.

X = \frac{a + b}{a - b}, Y = \frac{b + c}{b - c}, Z = \frac{c + a}{c - a}

.
What is tha value of XY + YZ + ZX ?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Arithmetic Progression

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Selecting Consecutive Terms in A.P

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon