MyQuestionIcon

1

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

Linear Dependence and Independence of Vectors

If b and c ar...

Question

If $\to b and \to c$ are two non-collinear unit vectors and $\to a$ is any vector, then $(\to a \cdot \to b) \to b + (\to a \cdot \to c) \to c + \frac{\to a \cdot (\to b \times \to c)}{| \to b \times \to c |^{2}} (\to b \times \to c) =$

A

\to a

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

B

\to b

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

C

\to c

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

D

\to a + \to b + \to c

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

Open in App

Solution

The correct option is A $\to a$
Let $\to b =^i, \to c =^j$
$∴ | \to b \times \to c | = |^k | = 1$
again, let $a = a_{1}^i + a_{2}^j + a_{3}^k$
Now,
$\to a \cdot \to b = \to a \cdot^i = a_{1}, \to a \cdot \to c = \to a \cdot^j = a_{2}$
and $\to a \cdot \frac{\to b \times \to c}{| \to b \times \to c |} = \to a \cdot^k = a_{3}$
$∴ (\to a \cdot \to b) \to b + (\to a \cdot \to c) \to c + \to a \cdot \frac{\to b \times \to c}{| \to b \times \to c |} (\to b \times \to c)$
$= a_{1} \to b + a_{2} \to c + a_{3} (\to b \times \to c) = a_{1}^i + a_{2}^j + a_{3}^k = \to a$

Suggest Corrections

thumbs-up

13

Similar questions

b

c

are any two non-collinear vectors, and

a

is any vector, then

(a \cdot b) b + (a \cdot c) c + \frac{a \cdot (b \times c)}{{| b \times c |}^{2}} (b \times c)

b

c

are any two non-collinear unit vecators and

a

is nay vector, then

(a . b) b + (a . c) c + \frac{a . (b + c)}{{| b + c |}^{2}} (b \times c) =

b

c

are any two non-collinear unit vectors and

a

is any vector, then

(a . b) b + (a . c) + \frac{a . b \times c}{| b \times c |} . (b \times c)

\to b

\to c

are non-zero and non-collinear vectors,

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

= (4 - 2 x - sin y) \to b + (x^{2} - 1) \to c

(\to c \cdot \to c) \to a = \to c

a, b, c

be three non-zero vectors such that no two of these are collinear. If the vectors

a + 2 b

is collinear with

c

b + 3 c

is collinear with

a

λ

being some non-zero scalar), then

a + 2 b + 6 c

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Linear Dependence and Independence of Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon