Let A¯=ai^+bj^+ck^ be a unit vector and B¯ is another vector in R3 such that |A¯×B¯|=1,C¯=13(2i^+2j^−k^) and (A¯×B¯)⋅C¯=1,then which of the following statement(s) is(are) correct?

C¯=A¯×B¯⇒A¯.C¯=0,2a+2b−c=0For A and B; a+b+c=0⇒c=0,a+b=0As a2+b2+c2=1,⇒{(12,−12,0)(−12,12,0)For (C,D);a2+b2+c2=1, 2a+2b=cAre not satisfied for any triplets of integers

Let A¯=ai^+bj^+ck^ be a unit vector and B¯ is another vector in R3 such that |A¯×B¯|=1,C¯=13(2i^+2j^−k^) and (A¯×B¯)⋅C¯=1,then which of the following statement(s) is(are) correct?

C¯=A¯×B¯⇒A¯.C¯=0,2a+2b−c=0For A and B; a+b+c=0⇒c=0,a+b=0As a2+b2+c2=1,⇒{(12,−12,0)(−12,12,0)For (C,D);a2+b2+c2=1, 2a+2b=cAre not satisfied for any triplets of integers

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Let $\bar{A} = a \hat{i} + b \hat{j} + c \hat{k}$ be a unit vector and $\bar{B}$ is another vector in R³ such that $| \bar{A} \times \bar{B} | = 1, \bar{C} = \frac{1}{3} (2 \hat{i} + 2 \hat{j} - \hat{k}) and (\bar{A} \times \bar{B}) \cdot \bar{C} = 1,$ then which of the following statement(s) is(are) correct?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

If $\bar{A}$ lies in the plane $x + y + z = 2023$ then there are exactly two choices for $\bar{A}$

If $\bar{A}$ lies in the plane $x + y + z = 2023$ then there are exactly 4 choices for $\bar{A}$

If $a, b, c \in I,$ then there is no such vector $\bar{A}$

If $a, b, c \in I$ , then there are infinitely many choices for $\bar{A}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\bar{C} = \bar{A} \times \bar{B} \Rightarrow \bar{A} . \bar{C} = 0, 2 a + 2 b - c = 0$
For A and B; $a + b + c = 0 \Rightarrow c = 0, a + b = 0$
As $a^{2} + b^{2} + c^{2} = 1, \Rightarrow {\begin{cases} (\frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}}, 0) \\ (- \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0) \end{cases}$
For (C,D); $a^{2} + b^{2} + c^{2} = 1, 2 a + 2 b = c$
Are not satisfied for any triplets of integers