87803 If the vectors \(\vec{c}, \vec{a}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(\vec{b}=\hat{j}\) are such that \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{c}}\) and \(\vec{b}\) form a right handed system, then \(\overrightarrow{\mathbf{c}}\) is

87821 If \(a, b, c\) are non coplanar vectors, then the point of intersection of the line passing through the points \(2 a+3 b-c, 3 a+4 b-2 c\) with the line joining the points \(a-2 b+3 c, a-6 b+6 c\) is

87804 Let \(a, b\) and \(c\) be three unit vectors such that \(a\) \(+\mathbf{b}+\mathbf{c}=\mathbf{0}\). If \(\boldsymbol{\lambda}=\mathbf{a} . \mathbf{b}+\mathbf{b} . \mathbf{c}+\mathbf{c} . \mathbf{a}\) and \(\mathbf{d}=\mathbf{a} \times \mathbf{b}\) \(+b \times c+c \times a\), then the ordered pair, \((\lambda, d)\) is equal to

87805 Let \(u, v\), w be such that \(|u|=1,|v|=2,|w|=3\). If the projection \(v\) along \(u\) is equal to that of \(w\) along \(u\) and \(v, w\) are perpendicular to each other, then \(|\mathbf{u}-\mathbf{v}+\mathbf{w}|\) equal to

87803 If the vectors \(\vec{c}, \vec{a}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(\vec{b}=\hat{j}\) are such that \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{c}}\) and \(\vec{b}\) form a right handed system, then \(\overrightarrow{\mathbf{c}}\) is

87821 If \(a, b, c\) are non coplanar vectors, then the point of intersection of the line passing through the points \(2 a+3 b-c, 3 a+4 b-2 c\) with the line joining the points \(a-2 b+3 c, a-6 b+6 c\) is

87804 Let \(a, b\) and \(c\) be three unit vectors such that \(a\) \(+\mathbf{b}+\mathbf{c}=\mathbf{0}\). If \(\boldsymbol{\lambda}=\mathbf{a} . \mathbf{b}+\mathbf{b} . \mathbf{c}+\mathbf{c} . \mathbf{a}\) and \(\mathbf{d}=\mathbf{a} \times \mathbf{b}\) \(+b \times c+c \times a\), then the ordered pair, \((\lambda, d)\) is equal to

87805 Let \(u, v\), w be such that \(|u|=1,|v|=2,|w|=3\). If the projection \(v\) along \(u\) is equal to that of \(w\) along \(u\) and \(v, w\) are perpendicular to each other, then \(|\mathbf{u}-\mathbf{v}+\mathbf{w}|\) equal to

87803 If the vectors \(\vec{c}, \vec{a}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(\vec{b}=\hat{j}\) are such that \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{c}}\) and \(\vec{b}\) form a right handed system, then \(\overrightarrow{\mathbf{c}}\) is

87821 If \(a, b, c\) are non coplanar vectors, then the point of intersection of the line passing through the points \(2 a+3 b-c, 3 a+4 b-2 c\) with the line joining the points \(a-2 b+3 c, a-6 b+6 c\) is

87804 Let \(a, b\) and \(c\) be three unit vectors such that \(a\) \(+\mathbf{b}+\mathbf{c}=\mathbf{0}\). If \(\boldsymbol{\lambda}=\mathbf{a} . \mathbf{b}+\mathbf{b} . \mathbf{c}+\mathbf{c} . \mathbf{a}\) and \(\mathbf{d}=\mathbf{a} \times \mathbf{b}\) \(+b \times c+c \times a\), then the ordered pair, \((\lambda, d)\) is equal to

87805 Let \(u, v\), w be such that \(|u|=1,|v|=2,|w|=3\). If the projection \(v\) along \(u\) is equal to that of \(w\) along \(u\) and \(v, w\) are perpendicular to each other, then \(|\mathbf{u}-\mathbf{v}+\mathbf{w}|\) equal to

87803 If the vectors \(\vec{c}, \vec{a}=x \hat{i}+y \hat{j}+z \hat{k}\) and \(\vec{b}=\hat{j}\) are such that \(\overrightarrow{\mathbf{a}}, \overrightarrow{\mathbf{c}}\) and \(\vec{b}\) form a right handed system, then \(\overrightarrow{\mathbf{c}}\) is

87821 If \(a, b, c\) are non coplanar vectors, then the point of intersection of the line passing through the points \(2 a+3 b-c, 3 a+4 b-2 c\) with the line joining the points \(a-2 b+3 c, a-6 b+6 c\) is

87804 Let \(a, b\) and \(c\) be three unit vectors such that \(a\) \(+\mathbf{b}+\mathbf{c}=\mathbf{0}\). If \(\boldsymbol{\lambda}=\mathbf{a} . \mathbf{b}+\mathbf{b} . \mathbf{c}+\mathbf{c} . \mathbf{a}\) and \(\mathbf{d}=\mathbf{a} \times \mathbf{b}\) \(+b \times c+c \times a\), then the ordered pair, \((\lambda, d)\) is equal to

87805 Let \(u, v\), w be such that \(|u|=1,|v|=2,|w|=3\). If the projection \(v\) along \(u\) is equal to that of \(w\) along \(u\) and \(v, w\) are perpendicular to each other, then \(|\mathbf{u}-\mathbf{v}+\mathbf{w}|\) equal to