Passing through the point be | 3D | JEE Mains 2026

Competishun Header

JEE-Main_2026

02-04-26_S1

Question

Let a line $L$ passing through the point $(1,1,1)$ be perpendicular to both the vectors $2 \hat{i}+2 \hat{j}+\hat{k}$ and $\hat{i}+2 \hat{j}+2 \hat{k}$. If $\mathrm{P}(\mathrm{a}, \mathrm{b}, \mathrm{c})$ is the foot of perpendicular from the origin on the line L , then the value of $34(a+b+c)$ is :

Select the correct option:

A

50

B

80

C

100

D

120

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

Q JEE MAIN 20262026

Given below are two statements
Statement I: $\mathrm{H}_2 \mathrm{O}$ molecules move from the chamber 1 to chamber 2 .
Statement II:...

JEE MainChemistryMedium

View Solution→

If the curve $y=f(x)$ passes through the point ( $1, \mathrm{e}$ ) and satisfies the differential equation $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $\stackrel{\mathbb{J}}{\mathrm{a}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\stackrel{\mathrm{b}}{\mathrm{b}}=3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\stackrel{n}{\mathrm{c}}$ is a vector such that $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $\alpha_1, \alpha_2, \ldots, \alpha_7$ be the roots of the equation $x^7+3 x^5-13 x^3-15 x=0$ and $...

JEE MainMathematicsEasy

View Solution→

$\lim _{x \rightarrow 2} \frac{\sin \left(x^3-5 x^2+a x+b\right)}{(\sqrt{x-1}-1) \log _e(x-1)}=m$, then $a+b+m$ is equal to :

JEE MainMathematicsMedium

View Solution→

QJEE Main 20232023

Let $\alpha=8-14 i, \quad A=\left\{z \in C: \frac{\alpha z-\bar{\alpha} \bar{z}}{z^2-(\bar{z})^2-112 i}=1\right\}$ and $B=\{z \in C:|z+3 i|=4\}$ Then $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $x=\{11,12,13, \ldots, 40,41\}$ and $Y=\{61,62,63, \ldots, 90,91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $\left\{a_k\right\}$ and $\left\{b_k\right\}, k \in N$, be two G.P.s with common ratio $r_1$ and $r_2$ respectively such that $a_1=b_1=4$...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $A$ be a symmetric matrix such that $|A|=2$ and $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

If the equation of the normal to the curve $y=\frac{x-a}{(x+b)(x-2)}$ at the point $(1,-3)$ is $x-4 y=13$, then the value...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $a_1=b_1=1$ and $a_n=a_{n-1}+(n-1), b_n=b_{n-1}+a_{n-1}, \forall n \geq 2$. If $\sum_{n=1}^{10} \frac{b_n}{2^n}$ and $T=\sum_{n=1}^8 \frac{n}{2^{n-1}}$, then $2^7(2 S-$ T )...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

A circle with centre $(2,3)$ and radius 4 intersects the line $x+y=3$ at the points $P$ and $Q$. If the...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

A triangle is formed by the tangents at the point $(2,2)$ on the curves $y^2=2 x$ and $x^2+y^2=4 x$, and...

JEE MainMathematicsEasy

View Solution→

Let a line $L$ passing through the point $(1,1,1)$ be perpendicular to both the vectors $2 \hat{i}+2 \hat{j}+\hat{k}$ and $...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is $\_\_\_\_$ .

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Consider a function $f: N \rightarrow R$, satisfying $f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2$ with $f(1)=1$. Then...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

Let $R$ be a relation defined on $N$ as a $R b$ is $2 a+3 b$ is a multiple of...

JEE MainMathematicsEasy

View Solution→

QJEE Main 20232023

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 ,...

JEE MainMathematicsEasy

View Solution→