Read the two statements and choose the correct option. I. The line r = ( i + 2 j) + λ(2 i - k) passes through (5, 2, 2). II. The Cartesian form of r = (2 i - k) + λ( j + 3 k) is (x - 2)/0 = y/1 = (z + 1)/3.

Question 50

MediumOriginal question

Read the two statements and choose the correct option.
I. The line $\vec{r} = (\hat{i} + 2\hat{j}) + \lambda(2\hat{i} - \hat{k})$ passes through $(5, 2, 2)$ .
II. The Cartesian form of $\vec{r} = (2\hat{i} - \hat{k}) + \lambda(\hat{j} + 3\hat{k})$ is $\frac{x - 2}{0} = \frac{y}{1} = \frac{z + 1}{3}$ .

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

I: $x = 1 + 2\lambda = 5$ needs $\lambda = 2$ , which gives $z = -2$ , not 2. False.
II: the point is $(2, 0, -1)$ and the direction ratios are $0, 1, 3$ . True.

Ten questions from Three-Dimensional Geometry, at your own pace.