New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Vector Algebra question

2023 · 13 Apr · Shift 2 · Q34

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

PYQ Library
JEE Main
Mathematics
Vector Algebra
2023 · 13 Apr · Shift 2 · Q34

Vector Algebra question

2023 · 13 Apr · Shift 2 · Q34

JEE MainMathematicsVector AlgebraMCQ+4 / −1

Let for a triangle

\mathrm{ABC}

,

\overrightarrow{\mathrm{AB}}=-2 \hat{i}+\hat{j}+3 \hat{k}\overrightarrow{\mathrm{CB}}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}\overrightarrow{\mathrm{CA}}=4 \hat{i}+3 \hat{j}+\delta \hat{k}

If

\delta \gt 0

and the area of the triangle

\mathrm{ABC}

is

5 \sqrt{6}

, then

\overrightarrow{C B} \cdot \overrightarrow{C A}

is equal to

A
60
B
54
C
120
D
108

More from Vector Algebra

Let $ABCD$ be a quadrilateral. If $E$ and $F$ are the mid points of the diagonals $(A B - B C) + (A D - D C) = k F E$ and $BD$ respectively and $(A B - B C) + (A D - D C) = k F E$ …2023 · MCQ
Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that $\frac{Q A}{A R} = \frac{R B}{B P} = \frac{P C}{C Q} = \frac{1}{2}$ . Then $\frac{A r e a ( Δ P QR )}{A r e a ( Δ A B C )}$ is equal…2023 · MCQ
Let $α = 4 i + 3 j + 5 k$ and $β = i + 2 j - 4 k$ . Let $β_{1}$ be parallel to $α$ and $β_{2}$ …2023 · MCQ
Let $a = i + 2 j + λ k, b = 3 i - 5 j - λ k, a . c = 7, 2 b . c + 43 = 0, a \times c = b \times c$ …2023 · Numerical
The vector $a = - i + 2 j + k$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $b$ . Then the projection of $3 a + 2 b$ …2023 · MCQ
If the vectors $a = λ i + μ j + 4 k$ , $b = - 2 i + 4 j - 2 k$ and $c = 2 i + 3 j + k$ are coplanar and…2023 · MCQ
If $a = i + 2 k, b = i + j + k, c = 7 i - 3 j + 4 k, r \times b + b \times c = 0$ …2023 · MCQ
Let $a = 4 i + 3 j$ and $b = 3 i - 4 j + 5 k$ . If $c$ is a vector such that $c . (a \times b) + 25 = 0, c . (i + j + k) = 4$ …2023 · MCQ