When vector A→=2i^+3j^+2k^ is subtracted from vector B→, it gives a vector equal to 2j^. Then the magnitude of vector B→ will be:

Correct answer: (D) √33. It is given that A→=2i^+3j^+2k^. By the given condition, B→-(2i^+3j^+2k^)=2j^ ⇒B→=2i^+5j^+2k^ The magnitude is given by the formula,B→=√(B^2x+B^2y+B^2z) ⇒|B→|=√(4+25+4)=√33

Q68 / 90 · JEE Main 2023 (11 Apr Shift 2) · Physics

When vector $\vec{A} = 2 \hat{i} + 3 \hat{j} + 2 \hat{k}$ is subtracted from vector $\vec{B}$ , it gives a vector equal to $2 \hat{j}$ . Then the magnitude of vector $\vec{B}$ will be:

A
$\sqrt{5}$
B
$3$
C
$\sqrt{6}$
Correct answer
D
$\sqrt{33}$

Solution

It is given that $\vec{A} = 2 \hat{i} + 3 \hat{j} + 2 \hat{k}$ .
By the given condition,
$\vec{B} - (2 \hat{i} + 3 \hat{j} + 2 \hat{k}) = 2 \hat{j}$
$\Rightarrow \vec{B} = 2 \hat{i} + 5 \hat{j} + 2 \hat{k}$
The magnitude is given by the formula, $|\vec{B}| = \sqrt{{B^{2}}_{x} + {B^{2}}_{y} + {B^{2}}_{z}}$
$\Rightarrow | \vec{B} | = \sqrt{4 + 25 + 4} = \sqrt{33}$

Hence, the correct answer is option: 'D'.

Relevant Questions

Two particles are located at equal distance from origin. The position vectors of those are represented by and , respectively. If both the ve23 Jan, 2025 (M)Addition and Subtraction of Vectors
If and makes an angle with each other, then for The integer value of is ____09 Apr, 2024 (M)Addition and Subtraction of Vectors
The resultant of two vectors and is perpendicular to and its magnitude is half that of . The angle between vectors and is ______ .09 Apr, 2024 (E)Addition and Subtraction of Vectors
Three vectors and each of magnitude are acting as shown in figure. The resultant of the three vectors is . The value of is ________ .08 Apr, 2024 (M)Addition and Subtraction of Vectors
The angle between vector and the resultant of and is :05 Apr, 2024 (M)Addition and Subtraction of Vectors
Two forces and are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to 04 Apr, 2024 (M)Addition and Subtraction of Vectors