Vectors ai + bj + k and 2i - 3j + 4k are perpendicular to each other when 3a + 2b = 7, the ratio of a to b is x/2. The value of x is ____________. Numerical answer type. Work it out, then open the answer.

Answer: 1. Perpendicular: 2a - 3b + 4 = 0; also 3a + 2b = 7. Solving: a = 1, b = 2. a/b = 1/2 = x/2 Answer: x = 1

Vectors ai + bj + k and 2i - 3j + 4k are perpendicular to each other… | JEE Main 2023 (24 Jan, Shift 1)

Q17JEE Main 2023 · 24 JAN · SHIFT 1Medium

Scalar (Dot) Product

Vectors $a\hat{i} + b\hat{j} + \hat{k}$ and $2\hat{i} - 3\hat{j} + 4\hat{k}$ are perpendicular to each other when $3a + 2b = 7$ , the ratio of $a$ to $b$ is $\frac{x}{2}$ . The value of $x$ is ____________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 1

Perpendicular: $2a - 3b + 4 = 0$ ; also $3a + 2b = 7$ .
Solving: $a = 1$ , $b = 2$ .
$\frac{a}{b} = \frac{1}{2} = \frac{x}{2}$
Answer: $x = 1$

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