Let A = (i + j) and, B = (2i - j). The magnitude of a coplanar vector C such that A · C = B · C = A · B, is given by: (a) √(10/9) (b) √(5/9) (c) √(20/9) (d) √(9/12)

Answer: (b). A · B = 2 - 1 = 1. Let C = xi + yj. A · C = x + y = 1 and B · C = 2x - y = 1. x = 2/3, y = 1/3 ⇒ |C| = √(4/9 + 1/9) = √(5/9) So the answer is (b).

Let A = (i + j) and, B = (2i - j). The magnitude of a coplanar vector… | JEE Main 2018 (16 Apr, Shift 1)

Q24JEE Main 2018 · 16 APR · SHIFT 1Difficult

Scalar (Dot) Product

Let $\vec{A} = (\hat{i} + \hat{j})$ and, $\vec{B} = (2\hat{i} - \hat{j}).$ The magnitude of a coplanar vector $\vec{C}$ such that $\vec{A} \cdot \vec{C} = \vec{B} \cdot \vec{C} = \vec{A} \cdot \vec{B},$ is given by:

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Answer: (b)

$\vec{A} \cdot \vec{B} = 2 - 1 = 1$ . Let $\vec{C} = x\hat{i} + y\hat{j}$ .
$\vec{A} \cdot \vec{C} = x + y = 1$ and $\vec{B} \cdot \vec{C} = 2x - y = 1$ .
$x = \frac{2}{3},\ y = \frac{1}{3} \Rightarrow |\vec{C}| = \sqrt{\frac{4}{9} + \frac{1}{9}} = \sqrt{\frac{5}{9}}$
So the answer is (b).

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Scalar (Dot) Product question from JEE Main 2018 (16 Apr, Shift 1)

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