Question:
Which one of the following is a point on the straight line $\vec{r}=(13\hat{i}-14\hat{j}+23\hat{k})+\lambda(5\hat{i}-7\hat{j}-9\hat{k})$?
Which one of the following is a point on the straight line $\vec{r}=(13\hat{i}-14\hat{j}+23\hat{k})+\lambda(5\hat{i}-7\hat{j}-9\hat{k})$?
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The starting point $(\lambda=0)$ is usually given in the first part of the vector equation.
Updated On: Apr 28, 2026
- (13, -14, -23)
- (5, -7, -9)
- (23, -28, 7)
- (23, -28, 5)
- (13, 14, 23)
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Any point on the line is given by $(13+5\lambda, -14-7\lambda, 23-9\lambda)$.
Step 2: Analysis
Let's test $\lambda = 2$: $x = 13 + 5(2) = 23$. $y = -14 - 7(2) = -28$. $z = 23 - 9(2) = 5$.
Step 3: Conclusion
The point (23, -28, 5) satisfies the equation for $\lambda = 2$. Final Answer: (D)
Any point on the line is given by $(13+5\lambda, -14-7\lambda, 23-9\lambda)$.
Step 2: Analysis
Let's test $\lambda = 2$: $x = 13 + 5(2) = 23$. $y = -14 - 7(2) = -28$. $z = 23 - 9(2) = 5$.
Step 3: Conclusion
The point (23, -28, 5) satisfies the equation for $\lambda = 2$. Final Answer: (D)
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