87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)

87780 If \(\vec{a}\) is a non-zero vector of magnitude \(a\), then \(m \vec{a}\) is a unit vector if

87781 The unit vector which is orthogonal to the vector \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and is coplanar with vectors \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), is

87782 If \(C\) is the middle point of \(A B\) and \(P\) is any point outside \(A B\), then

87783 If \(\vec{a}=\hat{i}-\hat{j}-\hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}\) and \(p_1, p_2\) are the orthogonal projection vectors of \(\vec{a}\) on \(\vec{b}\) and \(\vec{b}\) on a respectively, then \(\left(\mathbf{p}_1+\mathbf{p}_2\right) \cdot\left(\mathbf{p}_1-\mathbf{p}_2\right)=\)