Let \overrightarrow{a}=2 \hat{i}-3 \hat{j}+4 \hat{k}, \overrightarrow{b}=\hat{i}+2 \hat{j}-\hat{k}, \overrightarrow{c}=3 \hat{i}+\hat{j}+\lambda \hat{k} be the co-terminal edges of a parallelepiped whose volume is 5 units. Then the value of \lambda is:

NIMCET 2025 Paper

Section: Mathematics

Question : 40 of 120

Marks: +1, -0

Let

{a}↖{→}=2 {i}↖{∧}-3 {j}↖{∧}+4 {k}↖{∧}, \;\; {b}↖{→}={i}↖{∧}+2 {j}↖{∧}-{k}↖{∧}, \;\; {c}↖{→}=3 {i}↖{∧}+{j}↖{∧}+λ {k}↖{∧}

be the co-terminal edges of a parallelepiped whose volume is 5 units. Then the value of

λ

is:

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