New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2019 · Shift 2 · Q27

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2019 · Shift 2 · Q27

Vector Algebra question

2019 · Shift 2 · Q27

JEE AdvancedMathematicsVector AlgebraNumerical+3 / −1

Let

\overrightarrow a = 2\widehat i + \widehat j - \widehat k

and

\overrightarrow b = \widehat i + 2\widehat j + \widehat k

be two vectors. Consider a vector c =

\alpha \overrightarrow a

+

\beta \overrightarrow b

,

\alpha

,

\beta \in

R. If the projection of

\overrightarrow c

on the vector (

\overrightarrow a

+

\overrightarrow b

) is

3\sqrt 2

, then the minimum value of (

\overrightarrow c-

(

\overrightarrow a \times \overrightarrow b

)).

\overrightarrow c

equals ................

Numerical answer

More from Vector Algebra

Let a and b be two unit vectors such that a . b = 0. For some x, y $\in$ R, let $c = x a + y b + a \times b$ . If | $c$ | = 2 and the vector c is…2018 · Numerical
Let O be the origin and let PQR be an arbitrary triangle. The point S is such that $O P$ . $O Q$ + $O R$ . $O S$ = $O R$ .…2017 · MCQ
Let O be the origin and $O X$ , $O Y$ , $O Z$ be three unit vectors in the directions of the sides $QR$ , $R P$ , $P Q$ respectively, of a…2017 · MCQ
Let $u = u_{1} i + u_{2} j + u_{3} k$ be a unit vector in $R^{3}$ and $w = \frac{1}{6} (i + j + 2 k) .$ Given that there exists a vector $v$ …2016 · Multiple correct
Match the following : Column $R^{2},$ (A) In $R^{2},$ If the magnitude of the projection vector of the vector $α i + β j$ on $3 i + j$ and If $α = 2 + 3 β,$ …2015 · MCQ
Let $Δ P QR$ be a triangle. Let $a = QR, b = R P$ and $c = P Q .$ If $a = 12, b = 43, b . c = 24,$ …2015 · Multiple correct
Suppose that $p, q$ and $r$ are three non-coplanar vectors in $R^{3}$ . Let the components of a vector $s$ along $p, q$ and $r$ …2015 · Numerical
Let $x, y$ and $z$ be three vectors each of magnitude $2$ and the angle between each pair of them is $\frac{π}{3}$ . If $a$ is a non-zero vector perpendicular to $x$ …2014 · Multiple correct