{"id":254338,"date":"2022-09-10T11:14:57","date_gmt":"2022-09-10T05:44:57","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-angle-between-two-vectors-given-by-6i%c2%af6j%c2%af%e2%88%923k%c2%af-and-7i%c2%af4j%c2%af4k%c2%af-is\/"},"modified":"2022-09-10T11:14:57","modified_gmt":"2022-09-10T05:44:57","slug":"the-angle-between-two-vectors-given-by-6i%c2%af6j%c2%af%e2%88%923k%c2%af-and-7i%c2%af4j%c2%af4k%c2%af-is","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the--angle-between-two-vectors-given-by-6i6j3k-----and\/","title":{"rendered":"The angle between two vectors given by 6i\u00af+6j\u00af\u22123k\u00af and 7i\u00af+4j\u00af+4k\u00af is"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The angle between two vectors given by 6i\u00af+6j\u00af\u22123k\u00af and 7i\u00af+4j\u00af+4k\u00af is","custom_permalink":"question\/physics\/the--angle-between-two-vectors-given-by-6i6j3k-----and\/"},"categories":[],"acf":{"question":"

The angle between two vectors given by 6<\/mn>i<\/mi>\u00af<\/mo><\/mover>+<\/mo>6<\/mn>j<\/mi>\u00af<\/mo><\/mover>\u2212<\/mo>3<\/mn>k<\/mi>\u00af<\/mo><\/mover><\/mrow><\/math> <\/xml>and 7<\/mn>i<\/mi>\u00af<\/mo><\/mover>+<\/mo>4<\/mn>j<\/mi>\u00af<\/mo><\/mover>+<\/mo>4<\/mn>k<\/mi>\u00af<\/mo><\/mover><\/mrow><\/math> <\/xml>is<\/p>","options":[{"option":"

cos<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>1<\/mn>3<\/mn><\/msqrt><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":false},{"option":"

cos<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>5<\/mn>3<\/mn><\/msqrt><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":false},{"option":"

sin<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>2<\/mn>3<\/mn><\/msqrt><\/mrow><\/mfrac><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":false},{"option":"

sin<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>5<\/mn><\/msqrt><\/mrow>3<\/mn><\/mfrac><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml> <\/p>","correct":true}],"solution":"

If the angle between the vectors is \u2018\u03b8<\/mi><\/math> <\/xml>\u2019 then <\/p>

cos<\/mi>\u03b8<\/mi>=<\/mo>A<\/mi>\u2192<\/mo><\/mover>.<\/mo>B<\/mi>\u2192<\/mo><\/mover><\/mrow>|<\/mo>A<\/mi>\u2192<\/mo><\/mover><\/mrow>|<\/mo><\/mrow>.<\/mo>|<\/mo>B<\/mi>\u2192<\/mo><\/mover><\/mrow>|<\/mo><\/mrow><\/mrow><\/mfrac><\/mrow><\/math> <\/xml><\/p>

\u21d2<\/mo>cos<\/mi>\u03b8<\/mi>=<\/mo>42<\/mn>+<\/mo>24<\/mn>\u2212<\/mo>12<\/mn><\/mrow>(<\/mo>36<\/mn>+<\/mo>36<\/mn>+<\/mo>9<\/mn><\/mrow><\/msqrt>)<\/mo>(<\/mo>49<\/mn>+<\/mo>16<\/mn>+<\/mo>16<\/mn><\/mrow><\/msqrt>)<\/mo><\/mrow><\/mfrac><\/mrow><\/math> <\/xml><\/p>

cos<\/mi>\u03b8<\/mi>=<\/mo>54<\/mn><\/mrow>(<\/mo>9<\/mn>)<\/mo>(<\/mo>9<\/mn>)<\/mo><\/mrow><\/mfrac>=<\/mo>2<\/mn>3<\/mn><\/mfrac><\/mrow><\/math> <\/xml><\/p>

\u2234<\/mo>sin<\/mi>\u03b8<\/mi>=<\/mo>5<\/mn><\/msqrt><\/mrow>3<\/mn><\/mfrac><\/mrow><\/math> <\/xml><\/p>

\u21d2<\/mo>\u03b8<\/mi>=<\/mo>sin<\/mi><\/mrow>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>5<\/mn><\/msqrt><\/mrow>3<\/mn><\/mfrac><\/mrow>)<\/mo><\/mrow><\/mrow><\/math> <\/xml><\/b><\/p>

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