If \overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}, \overrightarrow{b}=2 \hat{i}-\hat{j}+3 \hat{k} \text{ and } \overrightarrow{c}=\hat{i}-2 \hat{j}+\hat{k} then the vector of magnitude \sqrt{22} which is parallel to 2 \overrightarrow{a}-\overrightarrow{b}+3 \overrightarrow{c} is:

Correct Answer is : 3i∧−3j∧+2k∧

(\hat{i}-4 \hat{j}+2 \hat{k}) \sqrt{\frac{22}{21}}

(\hat{i}-4 \hat{j}-2 \hat{k}) \sqrt{\frac{22}{21}}

NIMCET 2025 Paper

Section: Mathematics

Question : 31 of 120

Marks: +1, -0

{a}↖{→}={i}↖{∧}+{j}↖{∧}+{k}↖{∧}, \;\; {b}↖{→}=2 {i}↖{∧}-{j}↖{∧}+3 {k}↖{∧} \;\; \;\text " and "\; \;\; {c}↖{→}={i}↖{∧}-2 {j}↖{∧}+{k}↖{∧}

then the vector of magnitude

{√{22}}

which is parallel to

2 {a}↖{→}-{b}↖{→}+3 {c}↖{→}

is:

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