Question
The value of $n$ so that vectors $2 \hat{i}+3 \hat{j}-2 \hat{k}, 5 \hat{i}+n \hat{j}+\hat{k}$ and $-\hat{i}+2 \hat{j}+3 \hat{k}$ may be coplanar, will be(A) 18(B) 28(C) 9(D) 36
Step 1
We know that three vectors are coplanar if the determinant of the matrix formed by their coefficients is zero. Show more…
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Key Concepts
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If the three vectors are coplanar, then value of ' $x^{\prime}$ is: $\overrightarrow{\mathrm{A}}=\hat{i}-2 \hat{j}+3 \hat{\mathrm{k}}$ $\vec{B}=x \hat{j}+3 \hat{k}$ $\vec{C}=7 \hat{i}+3 \hat{\jmath}-11 \hat{k}$ (a) $36 / 21$ (b) $-51 / 32$ (c) $51 / 32$ (d) $-36 / 21$
If the vectors $\vec{a}-2 \hat{i}-\hat{j}+\hat{k}, \vec{b}-\hat{i}+2 \hat{j}-3 \hat{k}$ and $\vec{c}-3 \hat{i}+\lambda \hat{j}+5 \hat{k}$ are coplanar, the value ol $\lambda$ is (a) $-1$ (b) 3 (c) $-4$ (d) $-\frac{1}{4}$
Vectors and Scalars
Section B
The vectors $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \quad 5 \hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}} \quad$ and $-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ are coplanar when ' $a$ ' is (a) $-9$ (b) 9 (c) $-18$ (d) 18
Vector Analysis
Round 2
Transcript
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