143593 If vectors \(\overrightarrow{\mathbf{P}}=\mathbf{a} \hat{\mathbf{i}}+\mathbf{a} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{Q}=\mathbf{a} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are perpendicular to each other, then the positive value of \(a\) is

143594 Two equal vectors have a resultant equal to either of them, then the angle between them will be

143596 Assertion: If \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\), then the angle between \(\vec{A}\) and \(\vec{B}\) is \(90^{\circ}\).
Reason: \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{A}}\)

143597 If \(\mathrm{A}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}\) and \(\mathrm{B}=7 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}\) then the vector having the same magnitude as \(B\) and parallel to \(A\) is-

143593 If vectors \(\overrightarrow{\mathbf{P}}=\mathbf{a} \hat{\mathbf{i}}+\mathbf{a} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{Q}=\mathbf{a} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are perpendicular to each other, then the positive value of \(a\) is

143594 Two equal vectors have a resultant equal to either of them, then the angle between them will be

143596 Assertion: If \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\), then the angle between \(\vec{A}\) and \(\vec{B}\) is \(90^{\circ}\).
Reason: \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{A}}\)

143597 If \(\mathrm{A}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}\) and \(\mathrm{B}=7 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}\) then the vector having the same magnitude as \(B\) and parallel to \(A\) is-

143593 If vectors \(\overrightarrow{\mathbf{P}}=\mathbf{a} \hat{\mathbf{i}}+\mathbf{a} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{Q}=\mathbf{a} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are perpendicular to each other, then the positive value of \(a\) is

143594 Two equal vectors have a resultant equal to either of them, then the angle between them will be

143596 Assertion: If \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\), then the angle between \(\vec{A}\) and \(\vec{B}\) is \(90^{\circ}\).
Reason: \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{A}}\)

143597 If \(\mathrm{A}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}\) and \(\mathrm{B}=7 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}\) then the vector having the same magnitude as \(B\) and parallel to \(A\) is-

143593 If vectors \(\overrightarrow{\mathbf{P}}=\mathbf{a} \hat{\mathbf{i}}+\mathbf{a} \hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{Q}=\mathbf{a} \hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are perpendicular to each other, then the positive value of \(a\) is

143594 Two equal vectors have a resultant equal to either of them, then the angle between them will be

143596 Assertion: If \(|\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}|=|\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}|\), then the angle between \(\vec{A}\) and \(\vec{B}\) is \(90^{\circ}\).
Reason: \(\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}=\overrightarrow{\mathbf{B}}+\overrightarrow{\mathbf{A}}\)

143597 If \(\mathrm{A}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}\) and \(\mathrm{B}=7 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}\) then the vector having the same magnitude as \(B\) and parallel to \(A\) is-