Two vectors are given by A =(3 i + j +3 k ) and B =(3 i +5 j -2 k ) . Find the third vector C if A +3 B - C =0 .

Correct answer: C. (12 i +16 j -3 k ) aligned & A +3 B - C =0 & 3 i + j +3 k +3(3 i +5 j -2 k )- C =0 & 12 i +16 j -3 k - C =0, C =12 i +16 j -3 k aligned

AIIMS 201827 May

Exam: AIIMS
Year: 2018
Date: 27 May
Subject: Physics
Chapter: Mathematics in Physics

AIIMS 2018 · 27 May · Physics · Mathematics in Physics

Two vectors are given by A =(3 i + j +3 k ) and B =(3 i +5 j -2 k )...

Two vectors are given by

\vec{A}=(3 \hat{i}+\hat{j}+3 \hat{k})

and

\vec{B}=(3 \hat{i}+5 \hat{j}-2 \hat{k})

. Find the third vector

\vec{C}

\vec{A}+3 \vec{B}-\vec{C}=0

Options

A $(12 \hat{i}+14 \hat{j}+12 \hat{k})$
B $(13 \hat{i}+17 \hat{j}+12 \hat{k})$
C $(12 \hat{i}+16 \hat{j}-3 \hat{k})$
D $(15 \hat{i}+13 \hat{j}+4 \hat{k})$

Correct answer

C. $(12 \hat{i}+16 \hat{j}-3 \hat{k})$

Step-by-step solution

\begin{aligned} & \text{ } \vec{A}+3 \vec{B}-\vec{C}=0 \\ & 3 \hat{i}+\hat{j}+3 \hat{k}+3(3 \hat{i}+5 \hat{j}-2 \hat{k})-\vec{C}=0 \\ & 12 \hat{i}+16 \hat{j}-3 \hat{k}-\vec{C}=0, \vec{C}=12 \hat{i}+16 \hat{j}-3 \hat{k}\end{aligned}

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