Distance, Position and Section Formula of Vector
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Vector Algebra

87699 The position vector of point \(A\) is \((4,2,-3)\). If \(p_1\) is perpendicular distance of \(A\) from XY-plane and \(p_2\) is perpendicular distance from \(\mathrm{Y}\)-axis, then \(\mathrm{p}_1+\mathrm{p}_2=\)

1 8
2 3
3 2
4 7
Vector Algebra

87700 What is the perpendicular distance between \(2 x\)
\(+2 y-z+1=0 \text { and } x+y-\frac{z}{2}+2=0 \text { ? }\)

1 \(\sqrt{5}\)
2 \(\sqrt{2}\)
3 2
4 1
Vector Algebra

87701 Find the distance between the planes \(\overrightarrow{\mathbf{r}}(2 \hat{i}-\hat{j}+3 \hat{k})=4\) and \(\overrightarrow{\mathbf{r}}(6 \hat{i}-3 \hat{j}+9 \hat{k})+13=0\)

1 \(\frac{5}{3(\sqrt{14})}\)
2 \(\frac{10}{3(\sqrt{14})}\)
3 \(\frac{25}{3(\sqrt{14})}\)
4 None of these
Vector Algebra

87702 If \(2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}\) are the position vectors of the points \(A\) and \(B\) respectively, \(C\) divides \(A B\) in the ratio \(2: 3\) and \(M\) is the mid-point of \(A B\), then 5 (position vector of \(C\) ) - 2 (position vector of \(\mathbf{M}\) ) \(=\)

1 \(5 \hat{i}-5 \hat{j}-3 \hat{k}\)
2 \(11 \hat{i}-13 \hat{j}-11 \hat{k}\)
3 \(5 \hat{i}+5 \hat{j}-3 \hat{k}\)
4 \(11 \hat{i}+13 \hat{j}-11 \hat{k}\)
Vector Algebra

87699 The position vector of point \(A\) is \((4,2,-3)\). If \(p_1\) is perpendicular distance of \(A\) from XY-plane and \(p_2\) is perpendicular distance from \(\mathrm{Y}\)-axis, then \(\mathrm{p}_1+\mathrm{p}_2=\)

1 8
2 3
3 2
4 7
Vector Algebra

87700 What is the perpendicular distance between \(2 x\)
\(+2 y-z+1=0 \text { and } x+y-\frac{z}{2}+2=0 \text { ? }\)

1 \(\sqrt{5}\)
2 \(\sqrt{2}\)
3 2
4 1
Vector Algebra

87701 Find the distance between the planes \(\overrightarrow{\mathbf{r}}(2 \hat{i}-\hat{j}+3 \hat{k})=4\) and \(\overrightarrow{\mathbf{r}}(6 \hat{i}-3 \hat{j}+9 \hat{k})+13=0\)

1 \(\frac{5}{3(\sqrt{14})}\)
2 \(\frac{10}{3(\sqrt{14})}\)
3 \(\frac{25}{3(\sqrt{14})}\)
4 None of these
Vector Algebra

87702 If \(2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}\) are the position vectors of the points \(A\) and \(B\) respectively, \(C\) divides \(A B\) in the ratio \(2: 3\) and \(M\) is the mid-point of \(A B\), then 5 (position vector of \(C\) ) - 2 (position vector of \(\mathbf{M}\) ) \(=\)

1 \(5 \hat{i}-5 \hat{j}-3 \hat{k}\)
2 \(11 \hat{i}-13 \hat{j}-11 \hat{k}\)
3 \(5 \hat{i}+5 \hat{j}-3 \hat{k}\)
4 \(11 \hat{i}+13 \hat{j}-11 \hat{k}\)
Vector Algebra

87699 The position vector of point \(A\) is \((4,2,-3)\). If \(p_1\) is perpendicular distance of \(A\) from XY-plane and \(p_2\) is perpendicular distance from \(\mathrm{Y}\)-axis, then \(\mathrm{p}_1+\mathrm{p}_2=\)

1 8
2 3
3 2
4 7
Vector Algebra

87700 What is the perpendicular distance between \(2 x\)
\(+2 y-z+1=0 \text { and } x+y-\frac{z}{2}+2=0 \text { ? }\)

1 \(\sqrt{5}\)
2 \(\sqrt{2}\)
3 2
4 1
Vector Algebra

87701 Find the distance between the planes \(\overrightarrow{\mathbf{r}}(2 \hat{i}-\hat{j}+3 \hat{k})=4\) and \(\overrightarrow{\mathbf{r}}(6 \hat{i}-3 \hat{j}+9 \hat{k})+13=0\)

1 \(\frac{5}{3(\sqrt{14})}\)
2 \(\frac{10}{3(\sqrt{14})}\)
3 \(\frac{25}{3(\sqrt{14})}\)
4 None of these
Vector Algebra

87702 If \(2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}\) are the position vectors of the points \(A\) and \(B\) respectively, \(C\) divides \(A B\) in the ratio \(2: 3\) and \(M\) is the mid-point of \(A B\), then 5 (position vector of \(C\) ) - 2 (position vector of \(\mathbf{M}\) ) \(=\)

1 \(5 \hat{i}-5 \hat{j}-3 \hat{k}\)
2 \(11 \hat{i}-13 \hat{j}-11 \hat{k}\)
3 \(5 \hat{i}+5 \hat{j}-3 \hat{k}\)
4 \(11 \hat{i}+13 \hat{j}-11 \hat{k}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Vector Algebra

87699 The position vector of point \(A\) is \((4,2,-3)\). If \(p_1\) is perpendicular distance of \(A\) from XY-plane and \(p_2\) is perpendicular distance from \(\mathrm{Y}\)-axis, then \(\mathrm{p}_1+\mathrm{p}_2=\)

1 8
2 3
3 2
4 7
Vector Algebra

87700 What is the perpendicular distance between \(2 x\)
\(+2 y-z+1=0 \text { and } x+y-\frac{z}{2}+2=0 \text { ? }\)

1 \(\sqrt{5}\)
2 \(\sqrt{2}\)
3 2
4 1
Vector Algebra

87701 Find the distance between the planes \(\overrightarrow{\mathbf{r}}(2 \hat{i}-\hat{j}+3 \hat{k})=4\) and \(\overrightarrow{\mathbf{r}}(6 \hat{i}-3 \hat{j}+9 \hat{k})+13=0\)

1 \(\frac{5}{3(\sqrt{14})}\)
2 \(\frac{10}{3(\sqrt{14})}\)
3 \(\frac{25}{3(\sqrt{14})}\)
4 None of these
Vector Algebra

87702 If \(2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}\) are the position vectors of the points \(A\) and \(B\) respectively, \(C\) divides \(A B\) in the ratio \(2: 3\) and \(M\) is the mid-point of \(A B\), then 5 (position vector of \(C\) ) - 2 (position vector of \(\mathbf{M}\) ) \(=\)

1 \(5 \hat{i}-5 \hat{j}-3 \hat{k}\)
2 \(11 \hat{i}-13 \hat{j}-11 \hat{k}\)
3 \(5 \hat{i}+5 \hat{j}-3 \hat{k}\)
4 \(11 \hat{i}+13 \hat{j}-11 \hat{k}\)